DESIGN OF A WALL CLOCK WITH AN ADHESIVE HANGER

by

Ilkin Hossoy

Kristi Schmidt

ME 599-2003-10

December 15, 2003

Final Report

ABSTRACT This study demonstrates an analytical approach to the design of a quartz wall clock with an adhesive hanger utilizing an engineering model, a microeconomic model, and a marketing model. Design requirements were defined and then an engineering model was constructed based on the physical and ergonomic design requirements. The engineering model was optimized to minimize the total weight of the clock. A microeconomic model was then built using the previously defined engineering model that approximated elasticities for product characteristics (face diameter and frame thickness) and price based on informal interviews and the profit was maximized. A conjoint analysis survey (n=30) was conducted to build the marketing model. This survey examined four product characteristics (face diameter, frame thickness, font style, and font size) plus price. Demand curves were obtained for each product characteristic and price and profit was maximized. Cluster analysis was used to define three market segments within the survey data. Individually optimized solutions that maximized profit were compared to a product family solution by introducing a commonality constraint. Also, production capacity was investigated when optimizing profit. Finally a business plan was written.

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TABLE OF CONTENTS LIST OF TABLES.......................................................................................................................... 4 LIST OF FIGURES ........................................................................................................................ 4 NOMENCLATURE ....................................................................................................................... 5 1. INTRODUCTION .................................................................................................................. 7

1.1 Product Design Problem and Challenge ......................................................................... 7 1.2 Design Requirements ...................................................................................................... 7 1.3 Product Development Process Model............................................................................. 7

1.3.1 Customer Demand .................................................................................................. 8 1.3.2 Customer Specifications (hypothesized)................................................................. 8 1.3.3 Producer Specifications (hypothesized).................................................................. 8 1.3.4 Prioritized Customer Specifications (hypothesized)............................................... 8 1.3.5 Conceptual Design – Analyze – Pick...................................................................... 8 1.3.6 Refine With Respect To Specifications .................................................................. 8

2. ENGINEERING DESIGN MODEL....................................................................................... 9 2.1 Product Decisions That Can Be Made at the Design Phase............................................ 9 2.2 Design Requirements ...................................................................................................... 9 2.3 Design Requirements Quantifiable Using Engineering Models..................................... 9 2.4 Design Optimization Problem......................................................................................... 9

2.4.1 Design Variables (x) ............................................................................................... 9 2.4.2 Design Parameters (p)........................................................................................... 10 2.4.3 Parameter Values .................................................................................................. 10 2.4.4 Objective Function................................................................................................ 11 2.4.5 Constraints ............................................................................................................ 11 2.4.6 Assumptions.......................................................................................................... 12

2.5 Design Optimization Model in Negative Null Form .................................................... 12 2.6 Solution......................................................................................................................... 14

3. MICROECONOMICS MODEL........................................................................................... 15 3.1 Competitive Products.................................................................................................... 15 3.2 Quality Function Deployment (QFD)........................................................................... 15 3.3 Related Patent Descriptions .......................................................................................... 16 3.4 Revenue Model ............................................................................................................. 17 3.5 Cost Model.................................................................................................................... 20

3.5.1 Fixed Cost ............................................................................................................. 20 3.5.2 Variable Cost ........................................................................................................ 22

3.6 Optimal Design Problem: Maximize Profit .................................................................. 23 4. MARKETING MODEL ....................................................................................................... 24

4.1 Market Size ................................................................................................................... 24 4.2 Functional Relationships............................................................................................... 24 4.3 Logit Model .................................................................................................................. 24 4.4 Demand Function.......................................................................................................... 27 4.5 Linearization of the Marketing Demand Model ........................................................... 28

5. PRODUCT FAMILY DESIGN............................................................................................ 31 5.1 Market Segments .......................................................................................................... 31

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5.2 Design Optimization Model for Market Segment 1 ..................................................... 31 5.3 Design Optimization Model for Market Segment 2 ..................................................... 32 5.4 Design Optimization Model for Market Segment 3 ..................................................... 32 5.5 Product Family Design Optimization Model................................................................ 33 5.6 Product Family Design Optimization Model with Capacity Constraint ....................... 34 5.7 Comparison of Platform Design to Individually Optimized Designs........................... 36

6. CONCLUSIONS................................................................................................................... 38 7. REFERENCES ..................................................................................................................... 39 APPENDIX 1: ORTHOGONAL ARRAY FOR SURVEY DESIGN ......................................... 40 APPENDIX 2: SAS CODE FOR SURVEY DESIGN................................................................. 47 APPENDIX 3: RAW SURVEY DATA ....................................................................................... 49 APPENDIX 4: DENDROGRAM FROM SPSS HIERARCHICAL CLUSTER ANALYSIS .... 49 APPENDIX 4: DENDROGRAM FROM SPSS HIERARCHICAL CLUSTER ANALYSIS .... 50 APPENDIX 5: DEMAND CURVES FOR THREE MARKET SEGMENTS............................. 51 APPENDIX 6 : BUSINESS PLAN .............................................................................................. 54

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LIST OF TABLES Table 1: Summary of U.S. patent search of similar products ....................................................... 17 Table 2: Product Cost Components by Fixed and Variable Costs [21] ........................................ 21 Table 3: Product characteristics and their levels for the discrete choice analysis ........................ 25 Table 4: Levels for frame thickness and font size in terms of face diameter ............................... 25 Table 5: Product characteristic levels and corresponding beta values.......................................... 25 Table 1: Total profit at various capacities..................................................................................... 35 Table 7: Optimal solutions for each design model ....................................................................... 36

LIST OF FIGURES

Figure 1: Product development process model............................................................................... 7 Figure 2: Example of circular wall clock [2] .................................................................................. 8 Figure 3: House of Quality ........................................................................................................... 16 Figure 4: Demand curve for price................................................................................................. 18 Figure 5: Demand curve for face diameter ................................................................................... 18 Figure 6: Demand curve for frame thickness................................................................................ 19 Figure 7: Demand curve w.r.t. face diameter................................................................................ 26 Figure 8: Demand curve w.r.t. frame thickness ............................................................................ 26 Figure 9: Demand curve w.r.t. font size........................................................................................ 26 Figure 10: Demand curve w.r.t. price ........................................................................................... 26 Figure 11: Demand w.r.t. font style .............................................................................................. 27 Figure 1: Segment 1 face diameter demand curve........................................................................ 51 Figure 2: Segment 1 frame thickness demand curve .................................................................... 51 Figure 3: Segment 1 font size demand curve................................................................................ 51 Figure 4: Segment 1 price demand curve ..................................................................................... 51 Figure 5: Segment 1 font style demand ........................................................................................ 51 Figure 6: Segment 2 face diameter demand curve........................................................................ 52 Figure 7: Segment 2 frame thickness demand curve .................................................................... 52 Figure 8: Segment 2 font size demand curve................................................................................ 52 Figure 9: Segment 2 price demand curve ..................................................................................... 52 Figure 10: Segment 2 font style demand ...................................................................................... 52 Figure 11: Segment 3 face diameter demand curve...................................................................... 53 Figure 12: Segment 3 frame thickness demand curve .................................................................. 53 Figure 13: Segment 3 font size demand curve.............................................................................. 53 Figure 14: Segment 3 price demand curve ................................................................................... 53 Figure 15: Segment 3 font style demand ...................................................................................... 53

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NOMENCLATURE ( )f x objective function ( )g x inequality constraint ( )h x equality constraint

p price 0p price of the baseline design

1p material of clock frame, clock face, back cover plate, face plate

2p material of face cover

3p cost of plastic

4p height of quartz movement

5p width of quartz movement

6p depth of quartz movement

7p weight capacity of the mounting square

8p maximum allowable weight to be carried by mounting squares

9p cost of quartz movement

10p cost of the mounting square

11p density of the plastic used

12p weight of the quartz movement and the AA battery

13p minimum thickness of plastic

14p threshold viewing distance at 20.31 feet q quantity

1x diameter of clock face

2x total clock diameter

3x depth of clock

4x thickness of clock face

5x thickness of clock face cover

6x thickness of clock frame

7x thickness of back cover plate

8x length of the edge of the mounting squares

9x length of the hour hand

10x width of the hour and minute hands

11x length of the minute hand

12x length of the second hand

13x width of the second hand

1z face diameter

5

01z face diameter of the baseline design

2z frame thickness

02z frame thickness of the baseline design

3z font size

03z font size of the baseline design

4z font style C total cost

0C fixed cost

1C variable cost R revenue V volume of the total plastic used

1a Legibility of the clock face

2a weight of the clock

3a aesthetic appeal of the clock

4a functionality of the clock

Pλ price sensitivity

1zλ sensitivity to face diameter

2zλ sensitivity to frame thickness

3zλ sensitivity to font size θ intercept Π profit

6

1. INTRODUCTION

1.1 Product Design Problem and Challenge We want to design a quartz wall clock that appeals to potential buyers (i.e. is economical as well as functional). The design targets user’s from the general population for use in the household environment. Potential tradeoffs include size vs. functionality (a small clock may be hard to read and a large clock may be bulky), size vs. cost (a large clock may be more expensive), appearance vs. functionality (a very beautiful clock with lavish design may be cluttered and difficult to read), and appearance vs. cost (a beautiful design that is complicated may have higher production and material costs). Therefore, our major considerations are size, weight, and appearance with respect to functionality and cost. We will adopt the viewpoint of the assembler of the product. The clock will have an adhesive hanger that makes it possible to hang it on a wall without needing to drill a hole in the wall. This gives the user the flexibility to rearrange the room and move the clock, if desired. The adhesive hanger will be especially preferred for rental homes. Such a hanger will introduce additional constraints on the weight of the clock. The clock will also need to be readable from all parts of the room by a seated average household user with normal or corrected to normal vision. The average required distance floor to wall distance based on interview and random sampling of living room/kitchen arrangements is 20 feet. The average height of a wall clock in the home is 6 feet from the center of the clock to the floor. Eye level for a seated person with 50% stature (averaging over male and female) is approximately 29.82 inches [1]. This makes the average maximum total viewing distance from the user’s eye to the center of the clock is 20.31 feet.

1.2 Design Requirements We consider the following requirements for the design of the wall clock:

- Clock design accommodates a given quartz movement and selected hands. - The orientation of the dial is consistent with user expectations (i.e. “12” is on the top and

“6” is on the bottom). - The user must be able to tell the time from the clock (i.e. the user must be able to see the

hands, differentiate between the hour and minute hands, and read the numbers, if applicable).

- The adhesive clock hanger is sufficient to support the weight of the clock.

1.3 Product Development Process Model Figure 1 illustrates the product development process model. Below, the model is applied to the wall clock and inputs and outputs are specified.

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Figure 1: Product development process model

ENGINEER

ENGINEER, DESIGNER

CUSTOMER DEMAND

CONCEPTUAL DESIGNS

CUSTOMER SPEC’S

PRODUCER SPEC’S

PRIORITIZE CUSTOMER

SPEC’S

ANALYZE

PICK

REFINE SPEC’S

DEFINE PARAMETERS

FORMULATE OBJ. FUN. AND CONSTRAINTS

OPTIMIZE

PRODUCE

SELL

CUSTOMER FEEDBACK

CUSTOMER CUSTOMER

PRODUCER

DESIGNER

MARKETING

MANUFACTURER

ENGINEER

7

1.3.1 Customer Demand A device that gives the time and hangs on the wall without having to drill a hole

1.3.2 Customer Specifications (hypothesized) - Ability to read/understand time - Lightweight - Aesthetic - Low price - Accurate - Long lasting/Reliable - Reliable hanger without the need to drill a hole in the wall

1.3.3 Producer Specifications (hypothesized) - Low cost - High return

1.3.4 Prioritized Customer Specifications (hypothesized) - Ability to read/understand time - Low price - Aesthetic - Accurate - Reliable hanger without the need to drill a hole in the wall - Light weight - Long lasting/Reliable

1.3.5 Conceptual Design – Analyze – Pick After considering a square, a circular and an abstract design, we selected a circular design. As adhesive hangers we will use 0.25 lb/inch2 mounting squares.

1.3.6 Refine With Respect To Specifications The design is a circular quartz wall clock with plain frame and vertically oriented numbers as in Figure 2. With the exception of the quartz movement, the design is solely plastic construction. The clock has a flat front surface. The remaining the flowchart elements (refine with respect to specifications, define parameters and formulate objective function and constraints) will be discussed later in the report.

Figure 2: Example of circular wall clock [2]

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2. ENGINEERING DESIGN MODEL

2.1 Product Decisions That Can Be Made at the Design Phase The decisions listed below should be made at the design phase of the wall clock. These decisions are the key determinants of the engineering, microeconomic and marketing models as described in detail throughout the report.

- Product dimensions - Materials (e.g. plastic or glass for clock face; wood, metal, or plastic for frame) - Internal components (battery operated Quartz movement, adhesive hanger, hands) - Aesthetics (design of clock face with style and size of numbers) - Ergonomics (legibility)

2.2 Design Requirements Main product characteristics can be expressed as functions of design variables as follows:

- Legibility: 1 (font size, font style, labeling, tick marks, hand lengths, hand widths)a f=

- Weight: 2 (material selection, internal components, diameters, thickness)a f=

- Aesthetic appeal: 3 (color, font size, font style, materials, hand lengths, hand widths)a f=

- Functionality: 4 (on/off switch included with the standard quartz movement, font size,

font style, labeling, tick marks, hand lengths and widths, type of hanger)a f=

2.3 Design Requirements Quantifiable Using Engineering Models The only product characteristic that is quantifiable via engineering models is the weight of the wall clock ( 2α ). Legibility and functionality can be quantified via ergonomic models and behavioral sciences. To quantify aesthetic appeal, preference models are needed. In this chapter, we develop the engineering model for the product weight.

2.4 Design Optimization Problem In order to develop an engineering model for the weight of the wall clock, first we need to define the design variables and parameters.

2.4.1 Design Variables (x) In this study, we consider the following 13 design variables to determine the design of the wall clock:

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1x : Diameter of clock face

2x : Total clock diameter

3x : Depth of clock

4x : Thickness of clock face

5x : Thickness of clock face cover

6x : Thickness of clock frame

7x : Thickness of back cover plate

8x : Length of the edge of the mounting squares

9x : Length of the hour hand

10x : Width of the hour and minute hands

11x : Length of the minute hand

12x : Length of the second hand

13x : Width of the second hand

2.4.2 Design Parameters (p) We consider the following quantities as design parameters:

1p : Material of clock frame, clock face, back cover plate, face plate

2p : Material of face cover (glass or plastic)

3p : cost of plastic

4p : Height of quartz movement

5p : Width of quartz movement

6p : Depth of quartz movement

7p : Weight capacity of the mounting square

8p : Maximum allowable weight to be carried by mounting squares

9p : Cost of quartz movement (includes clock movement with on/off switch, and clock hardware) [3][4]

10p : Cost of the mounting square

11p : Density of the plastic used

12p : Weight of the quartz movement and the AA battery [3][5]

13p : Minimum thickness of plastic

14p : Threshold viewing distance at 20.31 feet

2.4.3 Parameter Values The parameter values are determined as follows:

1p = plastic (polyurethane) [6]

2p = plastic (polyurethane [6])

3p = $0.125/inch3

10

4p = 2 1/8”

5p = 2 1/8”

6p = 5/8”

7p = 0.25 lb/inch2

8p = 2 lb

9p = $1.50 (for purchase of 100+ units)

10p = $0.04625/inch2 [7]

11p = 0.03613 lb/inch3 [8]

12p = 0.1117 lb

13p = 0.0625”

14p = 0.07195”

2.4.4 Objective Function For the engineering model, our objective is to minimize the total weight of the wall clock.

Minimize = total weight f

2.4.5 Constraints This section describes the constraints on the design variables:

- Lower bound of the clock face diameter (constrained by the need to see the second hand tick marks from the maximum average viewing distance):

14

14

1

120 2.5 2 2.5 7.231"

7.231"

p p

xπ

× ×+ × × =

≥ (1)

- Lower bound of the total diameter (constrained by the movement size): (2) 2 3.875"x ≥

- Lower bound of the clock depth (5/8” movement thickness + 17/32” min overall shaft length + 1/8” clearance + 1/8” thickness of clock face cover):

(3) 3 1.406"x ≥- Lower bound of the clock face thickness (constrained by the lack of rigidity of plastic

below a given thickness): 4 13x p≥ (4)

- Lower bound of the clock face cover thickness (constrained by the lack of rigidity of plastic below a given thickness):

5 13x p≥ (5) - Lower bound of the clock frame thickness (constrained by the lack of rigidity of plastic

below a given thickness): 6 13x p≥ (6)

- Lower bound of the back cover plate thickness (constrained by the lack of rigidity of plastic below a given thickness):

11

7 13x p≥ (7) - Constraint on the size of the square adhesive hanger:

82 2x x≤ (8) - Constraint on the weight and diameter of the clock:

(9)211 12 8 7V p p x p× + ≤ ×

- Upper bound of the total weight of the clock: (10) 11 12 8V p p p× + ≤

- Constraint on the length of the hour hand (based on a market sample of 25 clocks [5]): 9 0.2783 1x x= (11)

- Constraint on the length of the minute hand (based on a market sample of 25 clocks [5]): 11 10.4136x x= (12)

- Constraint on the length of the second hand (based on a market sample of 25 clocks [5]): 12 10.3767x x= (13)

- Constraint on the widths of the hour, minute, and second hands: 10 132x x≥ (14)

- Lower bound of the second hand width (size of minimum recognizable object by a person with normal vision at a distance of 20.31’):

13 142.5x p≥ (15) - Upper bound of the hour and minute hand widths (the minute hand should not block the

view of more than one tick mark): 10 142 2.5x p≤ × (16)

- Constraint on the clock face and total diameters: 2 1x x≥ (17)

2.4.6 Assumptions The engineering design model is based on the following assumptions:

- Varying diameters of the clock will not significantly alter the viewing distance of the seated observer.

- Weight of the clock hands is negligible. - Clock face and hands have sufficient luminance for readability. - Clock face and hands have sufficient contrast for readability. - “Normal vision” is defined as the ability to detect an object with 1 minute (0.01667°)

visual angle from a distance of 20 feet [9]. - An object should be 2.5 times larger than threshold size [9].

2.5 Design Optimization Model in Negative Null Form Equation 18 summarizes the engineering design optimization model in negative null form.

12

2 2 2 21 2 2 1

4 5 7 6 2 3

min ( ) 0.03613 0.1117where

( )( )4 4 4

f V

x x x xV x x x x x xπ π π π

= +

−= × × + + × × + × × + × × ×

x

6x

13

1 1 9

2 1 1

3 1 1

subject to: 0.2783 0: 0.4136 0: 0.3767 0

h x xh x xh x x

− +− +− +

1

2

===

1 1

2 2

3 3

4 4

5 5

6 6

7 7

8 2 8

29 8

10

11 10 13

12 13

1

: 7.231 0: 3.875 0: 1.406 0: 0.0625 0: 0.0625 0: 0.0625 0: 0.0625 0

: 2 0: 0.25 0.03613 0.1117 0: 0.03613 0.1117 2 0: 2 0: 0.1799 0

g xg xg xg xg xg xg x

g x xg x Vg Vg x xg xg

− + ≤− + ≤− + ≤− + ≤− + ≤− + ≤− + ≤

− + ≤

− + ++ − ≤

− + ≤− + ≤

3 10

14 1 2

: 0.3598 0: 0x

g x x− ≤− ≤

≤

(18)

2.6 Solution Excel Solver minimizes weight at 0.4620 pounds. The minimizer values are given in Equation 19.

1

2

3

4

5

6

7

8

9

10

11

12

13

( *) 0.4620* 9.700* 7.231* 7.231* 1.406* 0.0625* 0.0625* 0.0625* 0.0625* 2.185* 2.012* 0.3598* 2.991* 2.724* 0.1799

fVxxxxxxxxxxxxx

===============

x

(19)

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3. MICROECONOMICS MODEL

3.1 Competitive Products Three online merchants—Amazon [5], Home & Garden>Furniture & Décor>Home Décor>Clocks>Wall Clocks], Clocko [10], and TopClock.com [11] have a wide array of wall clock selection. We limit discussion of competitive products to battery operated quartz wall clocks. The following is a discussion of a typical clock produced by each of several competitors. Infinity Instruments Ltd. [5] [12]: According to their website [12], “Infinity Instruments fuses design innovation and quality to create contemporary, functional accessories to decorate and enrich the home. Infinity sells to the trade only.” This $29.99 [5] metal clock measures 9.5” in diameter and 2.75” thick with no second hand. This clock has tickmarks and retro aesthetic appeal. Polder [5] [13]: Polder sells clocks on their webpage [13] as well as to registered vendors. This $17.99 [5] silver-toned plastic clock measures 10” in diameter and 1.5” thick with a second hand. It weights 2 pounds and requires 1 AA battery. The face is glass crystal, has excellent legibility (although small numbers) and tickmarks, and has contemporary aesthetic appeal. Bulova [10] [14]: Founded in 1875, The Bulova Corporation is headquartered in New York and is part of the American-owned and operated Loews Corporation [14]. This $29.50 [10] “country casual” wall clock measures 10” in diameter and 1.5” thick. There is a wide metal frame, protective glass lens, verdigris finish, Roman numerals, and a second hand. Timeworks [10] [15]: Timeworks was established in 1995 and builds “unique, functional clocks that tell more than just time” [15]. Produced in Berkeley, CA, this $59.99 [11] “Paris Expo” wall clock is 14” in diameter and displays the Eiffel Tower on its face with traditional aesthetics. There is no second hand.

3.2 Quality Function Deployment (QFD) Quality function deployment (QFD) analysis [16] helps compare these competitive products with ours. Figure 3 shows the house of quality with customer needs in the left column, technical response in the top row, relationships in the center, technical correlations at the top, and customer ratings in the planning matrix to the right for our product as compared to four of our competitors.

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Figure 3: House of Quality

3.3 Related Patent Descriptions A United States patent search was conducted using the United States Patent and Trademark Office online database [17]. The database searches from 1790 to present and our search terms were “TTL/quartz” AND “clock.” The search returned 52 patents, but only 17 were relevant to our project. These 17 patents were reviewed and are summarized in Table 1. We wondered if we could find out which patents were used in the quartz movement that we selected for our internal components. So we emailed Innovation Specialities, Inc. at clockparts@comcast.net [18]. We asked “what U.S. patent(s) the design is based on,” and got a response. The response was as following:

After 30 years in the business I rarely get new questions, but this sure is one. To the best of my knowledge our movements are not manufactured under a patent. There must be over 100 companies manufacturing quartz movements around the world and the only time I ever saw anything referring to a patent was on a very odd Swiss design from the 1990's. Regards, Mike Brosman Innovation Specialties Inc.

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Table 1: Summary of U.S. patent search of similar products

Pat. No. 3,939,644 – Circuit arrangement for controlling the running of a quartz-controlled electric clock Pat. No. 3,943,695 – Quartz crystal controlled timekeeping apparatus Pat. No. 3,945,194 – Electronic quartz clock with integrated circuits Pat. No. 3,973,148 – Quartz crystal vibrator unit Pat. No. 4,037,402 – Circuit arrangement for a quartz controlled electrical clock Pat. No. 4,087,957 – Movement construction for small size analog quartz timepiece Pat. No. 4,173,863 – Analog quartz timepiece Pat. No. 4,176,515 – Electronic clock, particularly a quartz clock Pat. No. 4,261,048 – Analog quartz timepiece Pat. No. 4,364,673 – Electric clock, particularly a quartz clock Pat. No. 4,367,956 – Clockwork of an electric quartz clock Pat. No. 4,417,820 – Time-keeping device, especially a quartz-controlled clock Pat. No. 4,445,785 – Electronic time setting for a quartz analog watch Pat. No. 4,508,458 – Electric clock movement, particularly a quartz clock movement Pat. No. D302,137 – Quartz clock movement Pat. No. D358,994 – Quartz clock with wildlife picture Pat. No. 6,359,840 – Microcontroller regulated quartz clock

3.4 Revenue Model In order to compute the revenue, we need the demand curve, i.e. the change in demand with respect to price. We collected data from 23 people, asking them the following question:

How much money would you be willing to pay for a wall clock for your home that has an adhesive hanger that won’t damage your wall? Assume you like how this clock looks, both in terms of design and size.

Figure 4 shows the demand curve for price that resulted from the data set. The demand curve has an intercept at 27.562 and a slope of -0.4984 which is the price sensitivity. We also need the sensitivities to product characteristics. We consider two main characteristics here: the clock face diameter ( 1z ) and the thickness of the clock frame ( 2z ). We collected data from 8 people. We asked them the following questions:

1) Pretend you're buying a wall clock that will be hung in your living room. You will view the clock from up to 20' away. What is the maximum clock face diameter you would tolerate?

2) Pretend you're buying a wall clock that will be hung in your living room. You will view the clock from up to 20' away. What is the maximum frame width around the clock face you would tolerate?

17

y = -0.4984x + 27.562

-5

0

5

10

15

20

25

0 20 40 60

Price

Qua

ntity

80

Figure 4: Demand curve for price

Figure 5 and Figure 6 show the demand curves for these characteristics. The slopes of the curves are the sensitivities for the characteristics based on 8 samples.

y = -0.5918x + 11.946

0

1

2

3

4

5

6

7

8

9

0 2 4 6 8 10 12 14 16 18 2

Face diameter

Qua

ntity

0

Figure 5: Demand curve for face diameter

18

y = -2.8709x + 8.1017

0

1

2

3

4

5

6

7

8

9

0 0.5 1 1.5 2 2.5 3

Frame thickness

Qua

ntity

Figure 6: Demand curve for frame thickness

Without conducting a discrete choice analysis, we won’t know the market share our clock will hold. We assume that in the year 2004 0.1% of the projected 107,672,899 United States households [19] will purchase a wall clock. When we scale the demand curves accordingly, the sensitivities represent the ones for the 107,670 people. So, the scaled sensitivities and the price intercept are:

1

2

23337965

38639

129020

p

z

z

λ

λ

λ

θ

=

=

=

=

(20)

The following equations relate the considered product characteristics to the design variables:

1 1

22 2

z x

1x xz

=−

= (21)

The next step is to express the revenue in terms of product characteristics and price.

(22)

2

2 2 11

Revenue = Price Quantity1 1 ( )

129020 1 1 ( )(7965 (7.231 ) 38639 (0 ))2333 2333 2333 2

p p p

R q q q

x xR q q x

θλ λ λ

×

= − + ∆

−= − + × − + × −

Tzλ z

q

19

3.5 Cost Model The total cost of the quartz wall clocks can be broken down into two components: initial investment fixed cost and operating variable cost. The operating variable cost is a function of the quantity produced and sold. Table 2 breaks down these fixed and variable costs into several components and subcomponents and also quantifies them. The following description elaborates on the source of the estimates. We assume that the quantity produced equals the quantity sold. We also assume that we are involved in all aspects of the manufacturing and sales of the quartz wall clocks. For example, we may sell these directly as an online merchant of amazon.com rather than in retail stores. The shipment cost (Table 2) of $3.34/clock reflects a free shipping option to consumers.

3.5.1 Fixed Cost Total product development and design: The product development and design cost includes marketing research, basic research on new product technologies, engineering analysis and optimization, design, and prototyping. The quartz wall clock requires extensive marketing research, yet less new product technologies due to the nature of the product. Our innovative components are the adhesive backing and the consideration of human factors issues. We will invest the equivalent of one full time researcher’s time for one month to product development and design. The researcher’s full time salary is $5,000 per month. Total manufacturing engineering: Once the product development and design is complete, manufacturing process research, process planning, and tool design must be carried out based upon the product design. An industrial engineer will carry out these tasks. The engineer will be given two weeks to complete this task. The equivalent salary is approximately $2,500. Total manufacturing: It is estimated that we will need two plastic injection molding machines and assembly line equipment. Lease price for each machine is estimated to be $1,000 per month and for the assembly line, $500 per month. For one year, this lease for two injection molding machines plus the assembly line will cost $30,000. Total inspection: Our inspection will not be done using automation, but solely by manpower as outlined below. Warehousing: We will need a warehouse of approximately 500 square feet to store the clocks before shipment. The monthly lease for industrial space would be approximately $3.50 per square foot [20]. Therefore, the warehouse would be approximately $21,000 per year. Inventory control: The staff engineer with a $60,000.00 annual salary will devote 1/12 time to inventory control by administrating inventory control software that will mange and control the inventory. The software costs $1,000.00. This amounts to a $6,000.00 cost over the course of one year. Overhead: A 1,000 square foot production facility will cost approximately $42,000 per year [20]. Utilities, support staff, management, and sales will be budgeted for an additional $10,000. Total overhead is estimated at $52,000 per year.

20

Table 2: Product Cost Components by Fixed and Variable Costs [21]

INITIAL INVESTMENT FIXED COST Product Marketing research Development Basic research on new product technologies and Design Engineering analysis and optimization Design drawings and specifications Prototype development Design testing Total Product Development and Design: $ 5,000.00 Manufacturing Manufacturing process research Engineering Process planning Tool design Total Manufacturing Engineering: $ 2,500.00 Manufacturing Parts fabrication (equipment) Assembly (assembly lines) Material handling (equipment) Production planning and control (computer resources) Total Manufacturing: $ 30,000.00 Inspection Inspection (inspection plan design and gages) Testing (test design and equipment) Total Inspection: $ 0.00 Distribution Warehousing $ 21,000.00 Inventory control $ 6,000.00 Total Distribution: $ 27,000.00 Overhead Factory (plant management, building, utilities, support staff) Corporate (management, sales, finance, legal, clerical, building, utilities) Total Overhead: $ 52,000.00 . TOTAL FIXED COST: $116,500.00 OPERATING VARIABLE COST = f(q) Materials Purchased composites and raw materials (polyurethane) $0.125/in3 ¥ V Transportation costs $0.18/lb¥(0.0361V+0.112) Receiving and inspection $0.10/lb¥(0.0361V+0.112) Internal quartz components $1.50 Total Materials: $ (0.1351¥V) + 1.531 Manufacturing Parts fabrication (labor and tooling) Assembly (tools and labor) Material handling (labor) Production planning and control (labor) Total Manufacturing: $ 0.75 Inspection Inspection (labor) Testing (labor) Total Inspection: $ 0.16 Distribution Shipment Total Distribution: $ 3.34 . TOTAL VARIABLE COST (per clock): $ (0.1351¥V) + 5.781

21

3.5.2 Variable Cost Purchased raw materials (polyurethane): Our estimated cost of polyurethane for injection molding is 12.5 cents per cubic inch. The required volume per clock is:

(23)

2 2 2 21 2 2 1

4 5 7 6 2 3( )( )

4 4 4x x x xV x x x x xπ π π π−

= × × + + × × + × × + × × × 6x x

Transportation: Railways, highways, waterways, oceans, and/or airways move materials efficiently. For our quartz wall clocks, we ship the quartz movements and raw materials via highway and cost figured according to weight. A 4,620 pound load (the weight of 10,000 clocks as defined in Assignment 2A) shipped from New Orleans, Louisiana, to Ann Arbor, Michigan, (1,050 miles [22]) would cost $831.23 according to American Freight Companies & Trucking Companies [23]. This averages $0.1799 per pound. Receiving and inspection: A worker that gets paid $10/hour unloads the materials from the truck and also inspects the boxes for damages. The worker unloads and inspects 100 total pounds of boxes per minute. This averages 10 cents per pound. Internal quartz components: The internal quartz components are purchased from Innovation Specialties, Inc. for $1.50 per quartz movement (includes clock movement with on/off switch, and clock hardware) [18]. Total Manufacturing (labor): Labor cost for manufacturing is estimated based upon a labor cost of $10/hour. Total time to manufacture and assemble each wall clock is approximately 3 minutes, but half is taken care of with automation. Therefore, the total manufacturing labor cost is 25 cents per clock. Total Manufacturing (tools): Tool cost for all manufacturing processes is based upon the injection molding and assembly. Injection molding offers high production rates but the tooling is costly [24]. We estimate that each tool costs $500 but on average will produce 1,000 parts. Per clock, this averages 50 cents. Total inspection: A worker that gets paid $10/hour places a AA battery into the clock, tests that it runs and also inspects the clock for manufacturing defects. This process takes the worker on average 1 minute per clock including transition time. This equates to 16 cents per clock. Total distribution: Amazon.com [5] charges $3.34 for shipping a 0.6 pound wall clock. Equation 24 summarizes the cost model that was laid out in Table 2.

(24)

[ ]0 1

Total cost = Fixed cost + Variable cost × Quantity

116500 (0.1351 ) 5.781C C C qC V q= + ×

= + × +

22

3.6 Optimal Design Problem: Maximize Profit The profit function is given as follows:

[ ]

2 2 11

129020 1 1 ( )(7965 (7.231 ) 38639 (0 ))2333 2333 2333 2

116500 (0.1351 ) 5.781

R Cx xq q x

V q

Π = −

−⎡ ⎤Π = − + × − + × −⎢ ⎥⎣ ⎦⎡ ⎤− + × +⎣ ⎦

q (25)

Note that we set the baseline values for the two product characteristics at . We got these values by maximizing the profit without including the terms about products characteristics.

1 27.231 and 0z z= =

Solving the optimization problem (see Equation 18 for constraints)

maxsubject to

( ) 0( ) 0

h xg x

Π

=≤

(26)

gives the following maximizer values:

1

2

3

4

5

6

7

8

9

10

11

12

13

( *) 1209763.90* 9.700* 7.231* 7.231* 1.406* 0.0625* 0.0625* 0.0625* 0.0625* 1.359* 2.012* 0.3598* 2.991* 2.724* 0.1799

6451027.65

fVxxxxxxxxxxxxx

qp

=================

x

(27)

23

4. MARKETING MODEL

4.1 Market Size The intended users for the quartz wall clock with an adhesive hanger are the general population of the United States. The clock is designed for people with a normal or corrected to normal vision for household use. To determine a market size for our product, we assume that the product will be sold exclusively in the United States. As in Section 3.4, we assume that there will be no less than 0.1% of all U.S. households that will purchase a wall clock for their home in a one year span of time. This assumption is intended to be more conservative than liberal because if we estimate conservatively, it is possible that more people will buy clocks rather than less. In 2004, the United States Census projects that there will be 107,672,899 households nationwide [19]. Therefore, estimating that 0.1% of all U.S. households will purchase a wall clock for their home sets our market size at 107,672.

4.2 Functional Relationships In addition to price, we are considering the following product characteristics as contributors to product utility:

1z : face diameter in inches

2z : frame thickness in inches as a proportion of face diameter

3z : font size in points as a proportion of face diameter

4z : font style We expect the following functional relationships of product utility with respect to price and the above product characteristics:

Price: Demand decreases as price increases (linear demand curve). Face diameter: Demand increases with face diameter until a certain value, and as face diameter increases further, demand starts decreasing (nonlinear demand curve). Frame thickness: Demand increases with frame thickness until a certain value, and as frame thickness increases further, demand starts decreasing (nonlinear demand curve). Font size: Demand increases with font size until a certain value, and as font size increases further, demand starts decreasing (nonlinear demand curve). Font style: Demand is higher for font styles that are easier to read (discrete design characteristic).

4.3 Logit Model The levels for the product characteristics chosen for the conjoint analysis are shown in Table 3. The levels for the frame thickness (thin and thick) and font size (small, medium and large) are encoded as proportions of the face diameter. Table 4 shows the corresponding proportions.

24

Table 3: Product characteristics and their levels for the discrete choice analysis

Characteristics Level 1 Level 2 Level 3 Price $10 $20 $30 Face diameter 8 inches 12 inches 16 inches Frame thickness None Thin Thick Font size Small Medium Large Font style Times New Roman

(serif) Arial

(sans-serif) Adolescence

(fancy)

Table 4: Levels for frame thickness and font size in terms of face diameter

None No frame Thin 3/32 face diameter (inches) Frame thickness Thick 6/32 face diameter (inches) Small 3/2 face diameter (points) Medium 11/4 face diameter (points) Font size Large 4 face diameter (points)

In order to collect preference data about the product characteristics at different levels, a discrete choice survey was designed and conducted. A full factorial experimental design with five product characteristics (including the price) at three levels each would have resulted in 3,125 different clock alternatives. Therefore, we used the commercially available computer statistical software SAS to generate an orthogonal design that resulted in 54 questions with three products and a no-choice alternative each. This orthogonal design and SAS code can be viewed in Appendix 1 and 2. A survey was created based upon this orthogonal design. Preference data was collected from 35 individuals that each took the survey and can be viewed in Appendix 3. This data was analyzed using the Logit model. Table 5 summarizes the beta values that were obtained for each product characteristic level using the maximum likelihood formula.

Table 5: Product characteristic levels and corresponding beta values

z1diameter

z2border

z3font size

z4font style

p price

1 2 3 4 5 k 8 none small Times N.R. 10 12 thin medium Arial 20

Leve

l 1 2 3 16 thick large Adolescence 30

Product characteristic

levels

-0.761 -0.162 -0.078 0.157 0.756 0.058 0.219 0.212 0.207 -0.193

Leve

l 1 2 3 0.208 -0.552 -0.629 -0.860 -1.059

Betas

Figures 1 to 4 show the demand curves with respect to the product characteristics. For frame thickness and font size, the demand function behaves as expected. It increases until a certain value, and then starts decreasing. Also the price curve demonstrates the hypothesized behavior. It

25

decreases almost linearly with increasing price. The demand change with respect to face diameter, however, is monotonically increasing within the given diameter range. We expected it to increase until a certain value, and to decrease as face diameter increases further. The reason for that might be that we didn’t include large enough face diameters in the survey to witness a downward slope in the demand curve.

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

8 12 1

di a me t e r ( i n. )

6

Figure 7: Demand curve w.r.t. face diameter

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1 2 3

bor de r ( none , t hi n, t hi c k )

Figure 8: Demand curve w.r.t. frame thickness

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1 2 3

f ont si z e ( sma l l , me di um, l a r ge )

Figure 9: Demand curve w.r.t. font size

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

10 20 30

pr i c e ( $ )

Figure 10: Demand curve w.r.t. price

Figure 11 shows the demand with respect to the font size. The choice of the font sizes was not random. We selected Arial which is a sans-serif font with a constant stroke width, Times New Roman which is a serif font with variable stroke width, and Adolescence which is a “fancy” font with irregular stroke widths. Figure 11 shows that users are almost indifferent between the sans-serif (Arial) and serif (Times New Roman) font styles, but they express a considerably lower demand for the “fancy” font style (Adolescence).

26

-1.2-1.0-0.8-0.6-0.4-0.20.00.20.40.60.81.01.2

1 2

font style (Times N. R., Arial, Adolescene)

Bet

a4

3

Figure 11: Demand w.r.t. font style

4.4 Demand Function Continuous functions of choice probabilities with respect to price and design characteristics were obtained using Excel’s spline add-in function [25] and Excel solver. The profit was maximized at $567,053.70 using the cost function from Equation 24 with the following additional constraints to limit the solution from extrapolating beyond the product characteristic levels of the survey:

1

2

3

8 160

321.5 410 30

z

z

zp

6≤ ≤

≤ ≤

≤ ≤≤ ≤

(28)

The maximum profit occurs with a 34.7% market share, which corresponds to 37,376 clocks sold. The optimum values for the price and the product characteristics are as follows:

1 2 313.73, 0, 2.446, 28.33z z z p= = = =

Solving the following marketing demand optimization problem (see Equation 18 for the previously defined constraints, and Equation 28 for the new constraints):

maxsubject to

( ) 0( ) 0

h xg x

Π

=≤

(29)

gives the following maximizer values:

27

1

2

3

4

5

6

7

8

9

10

11

12

13

( *) 567053.70* 31.54* 13.73* 13.73* 1.406* 0.0625* 0.0625* 0.0625* 0.0625* 2.237* 3.821* 0.3598* 5.678* 5.172* 0.1799

37376.428.33

fVxxxxxxxxxxxxx

qp

=================

x

(30)

The optimum solution for maximizing profit in the microeconomic demand model was presented in Equation 27. The maximum profit attainable according to the microeconomic demand model is $1,209,763.90. This occurs when 64,510 clocks are sold for $27.65 a piece. Each clock has a face diameter of 7.231 inches, no frame, and 10.85 point font. The maximum profit attainable according to the marketing demand model is $567,053.70. This occurs when 37,376 clocks are sold for $28.33 a piece. Each clock has a face diameter of 13.73 inches, no frame, and 33.58 point font. Considering the marketing demand model to be more rigorous, the demand of 33,376 clocks at $28.33 a piece yielding a $567,053.70 profit is assumed to be a better prediction.

4.5 Linearization of the Marketing Demand Model In our baseline design from the microeconomic demand model in Chapter 3 we used the following values for price and product characteristics:

(31) 0 0 01 2 3 07.231, 0, 1.5, 27.65z z z p= = = =

Note that we didn’t have the font size as a product characteristic in the previous calculations. Here we set the baseline value for font size at its lowest level. At the baseline design, the profit is $125,452.85 with 10.9% market share, which corresponds to 11,769 clocks sold. Using forward finite differences method, we calculated the following partial derivatives of the demand function with respect to price and the three product characteristics:

28

01

02

03

0

( ) 3524.20

( ) 99912.3

( ) 6161.07

( ) 820.257

qzqzqzqp

∂=

∂∂

=∂∂

=∂∂

= −∂

(32)

Now we can use the Taylor series approximation to linearize the demand function:

0 0 00 0 0 0 1 1 0 2 2 0 3 31 2 3

1 2 3

( , ) ( , ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

11769.5 820.257( 27.65) 3524.20( 7.231) 99912.3( 0) 6161.07( 1.5)[11769.5 22680.1 25483.5 0 9241.61] 820.257 3

q q q qq p q p p p z z z z z zp z z z

p z z zp

∂ ∂ ∂ ∂≅ + − + − + − + −

∂ ∂ ∂ ∂= − − + − + − + −= + − − − − +

0z z

1 2

1 2 3

524.20 99912.3 6161.07275.489 820.257 3524.20 99912.3 6161.07

z zp z z z

+ += − − + + +

3z

(33) So, the marketing demand model yields the following intercept and elasticity values:

1

2

3

275.489820.257

3524.20

99912.3

6161.07

p

z

z

z

θλ

λ

λ

λ

= −= −

=

=

=

(34)

Consider the intercept and elasticity values from the microeconomic demand model in Chapter 3 presented in Equation 20. In the marketing demand model the flatter price elasticity yields less change in demand as price changes compared to the microeconomic model. The trend is similar for the face diameter elasticity. The elasticities for frame thickness between the two models cannot be compared, because the marketing demand model considers frame thickness as a function of face diameter whereas in the microeconomic demand model, frame thickness is defined as an independent measure. Also, the marketing demand model has an additional elasticity for font size that wasn’t present in the microeconomic demand model. The additional elasticity for font size as well as the survey conducted in a more rigorous fashion makes the marketing demand model more precise. The demand varies between the marketing model and microeconomic model. The baseline was determined for the microeconomic demand model by optimizing the demand function without considering the product characteristic elasticities. Font size does not affect the solution using the microeconomic demand model, because it does not significantly change the production cost. Nonetheless, font size was assumed to be set at its minimum value for the optimal solution using

29

the microeconomic demand model. The microeconomic model optimized demand at 64,510 clocks yielding a profit of $1,209,763.90. With the same baseline design characteristic values, the marketing demand model predicts demand to be 11,769 clocks with a corresponding profit of $125,462.80. Again, considering the marketing demand model to be more rigorous, the demand of 11,769 is assumed to be a better prediction.

30

5. PRODUCT FAMILY DESIGN

5.1 Market Segments Three market segments were defined using hierarchical cluster analysis in the SPSS statistical software package. The data used was from the conjoint analysis survey. The dendrogram from the cluster analysis is found in Appendix 4 and illustrates two clear market segment clusters and a third segment that is made up of consumers that don’t clearly fit into the first two clusters. The first market segment is made up of 16 of the 35 survey respondents (45.7%), the second is made up of 12 of the 35 respondents (34.3%), and the third is made up of 7 of the 35 respondents (20.0%). The market size was defined as 107,672 households in Chapter 4 (0.1% of all United States households). Therefore, the estimated size of market segment 1 is 49,221 households, market segment 2 is 36,916 households, and market segment 3 is 21,534 households. The demand curves for each market segment are shown in Appendix 5. Recall that the demand curves for the entire market were presented in Chapter 4. Market segment 1 represents users with high price sensitivity as illustrated by the steep price demand curve relative to the other demand curves. Market segment 2 represents users who have a high sensitivity to the aesthetic appeal of the clock. Although the cluster analysis did not identify market segment 3 as a true cluster of users with similar preferences, the demand curves show that as a whole, market segment 3 has a high sensitivity to the size of the clock.

5.2 Design Optimization Model for Market Segment 1 The design optimization model from Chapter 4 was used to maximize profit for each market segment. For market segment 1, the profit was maximized at $282,018.03 with the following maximizer values corresponding to a $24.52 wall clock with a 12.99” face diameter, a 13.18” total diameter, a 31 points font size, and Times New Roman font style:

1

2

3

4

5

6

7

8

9

10

( *) 282018.03* 28.98* 12.99* 13.18* 1.406* 0.0625* 0.0625* 0.0625* 0.0625* 2.153* 3.616* 0.3598

fVxxxxxxxxxx

============

x

31

11

12

13

3

4

* 5.374* 4.895* 0.1799

2.385'Times New Roman '2688624.52

xxx

zzqp

======= (35)

5.3 Design Optimization Model for Market Segment 2 The design optimization model from Chapter 4 was used to maximize profit for each market segment. For market segment 2, the profit was maximized at $61,520.41 with the following maximizer values corresponding to a $30 wall clock with a 13.20” face diameter, a 13.39” total diameter, a 32 points font size, and Arial font style:

1

2

3

4

5

6

7

8

9

10

11

12

13

3

4

( *) 61520.41* 29.85* 13.20* 13.39* 1.406* 0.0625* 0.0625* 0.0625* 0.0625* 2.182* 3.674* 0.3598* 5.460* 4.973* 0.1799

2.394'Arial '881830.00

fVxxxxxxxxxxxxx

zzqp

===================

x

(36)

5.4 Design Optimization Model for Market Segment 3 The design optimization model from Chapter 4 was used to maximize profit for each market segment. For market segment 3, the profit was maximized at $100,604.40 with the following

32

maximizer values corresponding to a $30 wall clock with a 15.12” face diameter, a 15.31” total diameter, a 41 points font size, and Times New Roman font style:

1

2

3

4

5

6

7

8

9

10

11

12

13

3

4

( *) 100604.40* 38.47* 15.12* 15.31* 1.406* 0.0625* 0.0625* 0.0625* 0.0625* 2.451* 4.209* 0.3598* 6.256* 5.697* 0.1799

2.722'Times New Roman '1141330.00

fVxxxxxxxxxxxxx

zzqp

===================

x

(37)

5.5 Product Family Design Optimization Model A product family design optimization model was created that is based upon the previous design optimization model used in the above solutions. The new model optimizes clock designs for all three market segments by maximizing total profit and contains a new commonality constraint that sets the face diameter constant for all three designs. This solution is assumed to have a lower cost than producing each of the optimal designs for the three clocks because setting the face diameter constant would enable some of the same parts to be used for all three clocks. Therefore, each additional clock design produced carries a $5,000 additional cost due to increased product development and design and manufacturing engineering fixed costs. The optimal product family optimizes profit at $270,874.65 with the following maximizer values:

33

Product 1: Product 2: Product 3:

1

2

3

4

5

6

7

8

9

10

11

12

13

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

3

4

1

( *) 270874.65* 30.73* 13.41

* 13.60

* 1.406

* 0.0625

* 0.0625

* 0.0625

* 0.0625

* 2.211

* 3.732

* 0.3598

* 5.546

* 5.051

* 0.1799

2.385'Times New Roman '2685

fVx

x

x

x

x

x

x

x

x

x

x

x

x

zzq

===

=

=

=

=

=

=

=

=

=

=

=

=

===

x

1

324.73p =

1

2

3

4

5

6

7

8

9

10

11

12

13

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

3

4

2

2

( *) 61481.74* 30.73* 13.41

* 13.60

* 1.406

* 0.0625

* 0.0625

* 0.0625

* 0.0625

* 2.384

* 3.732

* 0.3598

* 5.546

* 5.051

* 0.1799

2.394'Arial '886930

fVx

x

x

x

x

x

x

x

x

x

x

x

x

zzqp

===

=

=

=

=

=

=

=

=

=

=

=

=

====

x

1

2

3

4

5

6

7

8

9

10

11

12

13

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

4

3

( *) 95610.57* 30.73* 13.41

* 13.60

* 1.406

* 0.0625

* 0.0625

* 0.0625

* 0.0625

* 2.479

* 3.732

* 0.3598

* 5.546

* 5.051

* 0.1799

2.722'Times New Roman '10569

fVx

x

x

x

x

x

x

x

x

x

x

x

x

zzq

===

=

=

=

=

=

=

=

=

=

=

=

=

===

x

3 30p = (38)

5.6 Product Family Design Optimization Model with Capacity Constraint

Now the same product family design optimization model as in the previous section is solved while introducing a capacity constraint. The capacity was set at 40,000 clocks per year. The design optimization model from Chapter 4 was used to maximize profit for each market segment. The optimal product family with capacity constraint optimizes profit at $251,375.48 with the following maximizer values:

34

Product 1: Product 2: Product 3:

1

2

3

4

5

6

7

8

9

10

11

12

13

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

3

4

1

( *) 251375.48* 29.55* 13.13

* 13.32

* 1.406

* 0.0625

* 0.0625

* 0.0625

* 0.0625

* 2.172

* 3.654

* 0.3598

* 5.430

* 4.946

* 0.1799

2.384'Times New Roman '2080

fVx

x

x

x

x

x

x

x

x

x

x

x

x

zzq

===

=

=

=

=

=

=

=

=

=

=

=

=

===

x

1

027.94p =

1

2

3

4

5

6

7

8

9

10

11

12

13

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

3

4

2

2

( *) 61514.31* 29.55* 13.13

* 13.32

* 1.406

* 0.0625

* 0.0625

* 0.0625

* 0.0625

* 2.384

* 3.654

* 0.3598

* 5.430

* 4.946

* 0.1799

2.394'Arial '880030.00

fVx

x

x

x

x

x

x

x

x

x

x

x

x

zzqp

===

=

=

=

=

=

=

=

=

=

=

=

=

====

x

1

2

3

4

5

6

7

8

9

10

11

12

13

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

4

3

( *) 93832.62* 29.55* 13.13

* 13.32

* 1.406

* 0.0625

* 0.0625

* 0.0625

* 0.0625

* 2.479

* 3.654

* 0.3598

* 5.430

* 4.946

* 0.1799

2.722'Times New Roman '10398

fVx

x

x

x

x

x

x

x

x

x

x

x

x

zzq

===

=

=

=

=

=

=

=

=

=

=

=

=

===

x

3 30p = (39)

Table 6: Total profit at various capacities

Product 1 Product 2 Product 3 Total capacity p q p q p q

Total profit Total q

35,000 $30 16,471 $30 8,605 $30 9,922 $362,101.05 35,000 40,000 $27.94 20,800 $30 8,800 $30 10,398 $406,722.40 40,000 45,000 $25.39 25,606 $30 8,856 $30 10,537 $427,009.96 45,000 50,000 $24.73 26,862 $30 8,869 $30 10,571 $427,967.22 46,304

Capacities in addition to 40,000 were optimized, and the corresponding prices, quantities and total profit for each capacity level are presented in Table 6. Note that the optimized solution at the 50,000 capacity is the same as the in the product family model without capacity constraint, because the optimal production level is less than the total capacity.

35

5.7 Comparison of Platform Design to Individually Optimized Designs

Table 7: Optimal solutions for each design model

Product family - unlimited

capacity Product family - capacity 40,000

Market segment

1

Market segment

2

Market segment

3 Product

1 Product

2 Product

3 Product

1 Product

2 Product

3

f(x*) profit ($) 282,018 61,520 100,604 270,875 61,482 95,611 251,375 61,514 93,833

V* volume (in3) 28.98 29.85 38.47 30.73 30.73 30.73 29.55 29.55 29.55

x1* face diameter 12.99 13.20 15.12 13.41 13.41 13.41 13.13 13.13 13.13

x2* total diameter 13.18 13.39 15.31 13.60 13.60 13.60 13.32 13.32 13.32

x3* clock depth 1.406 1.406 1.406 1.406 1.406 1.406 1.406 1.406 1.406

x4* face thickness 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625

x5* face cover thickness

0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625

x6* clock frame thickness

0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625

x7* back cover plate thickness

0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625

x8*

mounting square edge length

2.153 2.182 2.451 2.211 2.384 2.479 2.172 2.384 2.479

x9* hour hand length

3.616 3.674 4.209 3.731 3.732 3.732 3.654 3.654 3.654

x10*

hour and minute hand width

0.3598 0.3598 0.3598 0.3598 0.3598 0.3598 0.3598 0.3598 0.3598

x11* minute hand length

5.374 5.460 6.256 5.546 5.546 5.546 5.430 5.430 5.430

x12* second hand length

4.895 4.973 5.697 5.051 5.051 5.051 4.946 4.946 4.946

x13* second hand width

0.1799 0.1799 0.1799 0.1799 0.1799 0.1799 0.1799 0.1799 0.1799

z1

font size (points)

31 32 41 32 32 36 32 31 36

z2 font style 'Times N.R.' 'Arial' 'Times

N.R.' 'Times N.R.' 'Arial' 'Times

N.R.' 'Times N.R.' 'Arial' 'Times

N.R.'

q

quantity of clocks produced

26,886 8,818 11,413 26,853 8,869 10,569 20,800 8,800 10,398

p clock price ($) 24.52 30 30 24.73 30 30 27.94 30 30

Table 7 summarizes each of the optimized design models presented: each market segment solved independently, a product family solution, and a product family solution with a fixed capacity that limits optimal production. It is interesting to note that when a commonality constraint was added in the product family models setting face diameter equal, the optimization yielded three clocks having the same physical characteristics but varying font size and style rather than three clocks having the same face diameter with varying total diameters. It is interesting to compare the total profit for producing each of the three clocks that were optimized independently to the total profit for producing a product family. It was assumed that

36

producing each of the three independently optimized clocks would be more expensive than producing each of the three clocks optimized with a face diameter commonality constraint. It was estimated that producing each additional independently optimized clocks would cost $10,000 because there is no commonality among the clocks with respect to the parts produced. Total profit (including the $10,000 cost for each additional clock type produced) for the production of each of the three individually optimized clocks would be $424,142.82. An additional cost was added to both of the product family optimizations that essentially said that each additional clock product produced would carry an additional fixed $5,000 cost. Total profit (including the $5,000 cost for each additional clock type produced) for the production of the product family without any capacity constraints would be $427,996.95. If making a decision between producing the three independently optimized clocks and producing the product family, the obvious choice would be to select the production that yields the highest profit. This is the decision we make, although with one reservation. Our reservation has to do with the fact that we would be selling essentially the same clock but charging different prices for the clock. The physical attributes of each clock are the same, only the font size and style change. We wonder if people would really be willing to pay $5.27 more for a clock that has the same sized font (32 point) but different font style (‘Arial’ versus ‘Times New Roman’) or for a clock that has different font size (36 point versus 32 point) but the same font style (‘Times New Roman’). It is also interesting to look at the optimal production rates over various capacities. It was hypothesized that optimal solutions at low capacities may produce only one or two of the clock types rather than all three, but that never happened. Over capacities varying from 35,000 to 50,000, optimal production includes all three clock types.

37

6. CONCLUSIONS

It is interesting to compare solutions that maximized profit from the microeconomic model that included linear elasticity estimations for face diameter, frame width, and price; from the marketing model that included spline elasticity estimations for face diameter, frame width, font size, font style, and price; and from the product platform solutions with and without capacity constraints. We find our marketing model to be more rigorous than the microeconomic model because of the conjoint analysis data that support the elasticities and the greater number of product characteristics considered in the model. Furthermore, the product platform was created for three market segments that were not simply hypothesized, but that were obtained from a cluster analysis of the conjoint analysis survey data. Each model was created rigorously, yet each assumes no competition in the marketplace. Although there are no clocks on the market with an adhesive hanger to our knowledge, we do acknowledge the fact that this product will come against strong competition from traditionally hung quartz wall clocks that flood the market. The microeconomic and marketing models presented in this paper maximize profit and the results seem very promising for this new product, although the lack of market competition in the analysis seems unrealistic. A business plan presented in Appendix 6 outlines a realistic estimate of market share and profit for the first three years of production and sales of this product. Never in the first three years of production and sales does this quartz wall clock breakeven. Therefore, despite the promising returns on investment presented throughout the paper, as our models currently stand, we do not recommend to invest in the production of this clock. Before dismissing the idea of investment, we suggest that the cost model, in particular, be reexamined and, if needed, refined. We feel that estimations for this cost model may contain the most error that may be carried throughout the design optimization models.

38

7. REFERENCES

[1] Chaffin, D.B., Gunnar, B.J.A., and Martin, B.J. (1999). Occupational Biomechanics. New York: John Wiley & Sons, Inc., p.361.

[2] Wall Clocks [online]. http://store.yahoo.net/everythinghome/wallclock.html [3] Time Only Movements [online]. http://www.clockparts.com/quartz1.htm [4] Clock Hands [online]. http://www.clockparts.com/handindex.htm [5] Amazon [online]. http://www.amazon.com [6] Plastic Injection, Molded Plastics, Thermoplastics, Thermoset Plastics, Global Out Sourcing

[online]. http://www.plastics-source.com/Molding_Process.htm [7] 3M 1” SCOTCH Heavy Duty Mounting Squares, Pack of 16 at wholesale prices [online].

http://www.castlewholesalers.com/cat_productdetail.cfm?category=Hardware&subcat=Utility%20Tapes&subsubcat=Foam%20Tapes%20%26%20Squares&product_id=611111

[8] Densities of Various Materials [online]. http://www.mcelwee.net/html/densities_of_v arious_materials.html

[9] Konz, S. and Johnson, S. (2000). Work Design: Industrial Ergonomics. Scottsdale, AZ: Holcomb Hathaway Publishers.

[10] Wall Clocks – Clocko [online]. http://www.clocko.com/cat.asp/R=4/dept=clocks/cat=wall [11] Wall Clocks, Wall Clock Free Shipping [online]. http://www.hothotnews.com/store/Index-

Wall.htm [12] Infinity Instruments [online]. http://www.infinityinstruments.com/index.html [13] Polder Retail [online]. http://www.polder.com/cgi-bin/edmas_retail.mac/home [14] Bulova [online]. http://bulova.com/ [15] Timeworks Incorporated [online]. http://www.timeworksclocks.com/ [16] Cohen, L. (1995). Quality Function Deployment. Reading, MA: Addison-Wesley Publishing

Company. [17] Databases: Patent Grant and Patent Application [online]. http://www.uspto.gov/patft/inde

x.html [18] Time Only Movements [online]. http://www.clockparts.com/quartz1.htm [19] Projections of Households by Type: 1995 to 2010 [online]. http://www.census.gov/populati

on/projections/nation/hh-fam/table1n.txt [20] Wilkes-Barre Office Space for Lease [online].http://www.skylineleasing.com/tcn_features_

central/cent_6/index.html [21] Groover, M.P. (2001). Automation, Production Systems, and Computer-Integrated

Manufacturing. Upper Saddle River, NJ: Prentice Hall. [22] Mapquest Driving Directions [online]. http://www.mapquest.com/directions [23] American Freight Companies & Trucking Companies [online]. http://quote.freightcenter.co

m/quote.asp?id=71 [24] Kalpakjian, S. and Schmid, S. R. (2001). Manufacturing Engineering and Technology.

Upper Saddle River, NJ: Prentice Hall. [25] Interpolate, Cubic Spline and Curve Fit for Microsoft Excel [online]. http://www.netrax.net/

~jdavita/XlXtrFun/XlXtrFun.htm

39

APPENDIX 1: ORTHOGONAL ARRAY FOR SURVEY DESIGN font font

Obs Set Product diameter border Size Style price 1 1 P1 12 thin medium Times 10 2 1 P2 12 thick large Arial 20 3 1 P3 16 thick medium Times 10 4 2 P1 12 thick small Times 10 5 2 P2 16 thick medium Times 20 6 2 P3 12 thick small Fancy 30 7 3 P1 12 thick large Arial 30 8 3 P2 16 thick large Fancy 10 9 3 P3 12 none medium Times 20 10 4 P1 12 none large Times 10 11 4 P2 16 none small Arial 10 12 4 P3 16 none small Arial 20 13 5 P1 16 none small Arial 20 14 5 P2 16 thin small Fancy 30 15 5 P3 8 none large Fancy 20 16 6 P1 12 none small Fancy 20 17 6 P2 16 none large Fancy 20 18 6 P3 16 thick large Times 30 19 7 P1 8 thin large Times 20 20 7 P2 12 thin small Fancy 20 21 7 P3 12 none small Times 30 22 8 P1 16 thin small Times 30 23 8 P2 8 thin medium Fancy 10 24 8 P3 16 thick small Times 20 25 9 P1 16 thin large Times 10 26 9 P2 16 none large Fancy 10 27 9 P3 12 thin large Fancy 10 28 10 P1 8 none small Times 20 29 10 P2 12 none medium Arial 30 30 10 P3 8 thick small Arial 10 31 11 P1 16 thin medium Fancy 10 32 11 P2 8 thin small Times 20 33 11 P3 16 thin large Fancy 30 34 12 P1 8 none small Fancy 10 35 12 P2 8 thick medium Fancy 10 36 12 P3 16 none medium Fancy 10 37 13 P1 12 none medium Fancy 10 38 13 P2 8 thin large Times 30 39 13 P3 12 none small Times 20 40 14 P1 16 thick large Arial 10 41 14 P2 12 none medium Times 30 42 14 P3 16 thick large Times 20 43 15 P1 8 thin small Times 10 44 15 P2 16 thick small Times 30 45 15 P3 8 thin medium Times 20 46 16 P1 12 thick medium Arial 10 47 16 P2 12 thin small Fancy 10 48 16 P3 8 thick small Fancy 10 49 17 P1 16 thin medium Arial 30 50 17 P2 16 none small Arial 30 51 17 P3 12 thick small Times 30 52 18 P1 16 thin small Fancy 20 53 18 P2 16 none medium Times 20

40

54 18 P3 12 none medium Arial 20 55 19 P1 16 thin large Arial 20 56 19 P2 8 thin large Arial 30 57 19 P3 16 none medium Arial 10 58 20 P1 16 thick medium Arial 20 59 20 P2 8 thick medium Fancy 20 60 20 P3 8 thin medium Times 30 61 21 P1 12 thin small Arial 30 62 21 P2 12 thick small Times 10 63 21 P3 16 none large Arial 30 64 22 P1 8 none large Arial 10 65 22 P2 12 none large Times 20 66 22 P3 8 none medium Fancy 30 67 23 P1 8 thick large Fancy 30 68 23 P2 16 thin small Arial 20 69 23 P3 16 thick medium Fancy 20 70 24 P1 8 none medium Arial 20 71 24 P2 8 thick small Times 20 72 24 P3 16 thick small Arial 20 73 25 P1 8 thin medium Arial 10 74 25 P2 12 thin medium Arial 10

font font Obs Set Product diameter border Size Style price

75 25 P3 12 thin medium Arial 20 76 26 P1 8 none medium Fancy 30 77 26 P2 12 none small Fancy 10 78 26 P3 8 thin large Times 20 79 27 P1 12 thin medium Times 10 80 27 P2 8 none medium Fancy 30 81 27 P3 8 none large Arial 30 82 28 P1 12 thick small Fancy 30 83 28 P2 12 thin medium Arial 30 84 28 P3 8 none medium Times 30 85 29 P1 16 thick large Times 30 86 29 P2 8 thick small Times 30 87 29 P3 8 none small Fancy 10 88 30 P1 16 thick small Fancy 10 89 30 P2 8 thick large Arial 10 90 30 P3 8 thick large Arial 20 91 31 P1 12 thin large Fancy 20 92 31 P2 12 thick medium Fancy 30 93 31 P3 16 thin small Fancy 20 94 32 P1 8 thin medium Fancy 20 95 32 P2 16 thick large Arial 10 96 32 P3 8 none small Fancy 30 97 33 P1 16 none large Fancy 10 98 33 P2 16 thin medium Arial 20 99 33 P3 8 thin small Times 10 100 34 P1 8 thick small Arial 10 101 34 P2 8 none small Arial 20 102 34 P3 12 none large Times 10 103 35 P1 12 none large Arial 20 104 35 P2 8 thin medium Arial 10 105 35 P3 12 thick large Fancy 30 106 36 P1 8 thick large Fancy 30 107 36 P2 8 none medium Times 10 108 36 P3 12 thin small Arial 30

41

109 37 P1 8 thick small Arial 10 110 37 P2 16 thin large Fancy 30 111 37 P3 16 thin small Arial 30 112 38 P1 16 none medium Times 30 113 38 P2 16 thin large Times 10 114 38 P3 8 thick medium Arial 30 115 39 P1 12 thick large Times 20 116 39 P2 12 thin large Times 20 117 39 P3 8 thin large Arial 20 118 40 P1 16 none small Arial 20 119 40 P2 12 thick large Times 10 120 40 P3 12 thin small Times 10 121 41 P1 16 none medium Times 30 122 41 P2 12 thick medium Arial 20 123 41 P3 12 none large Fancy 20 124 42 P1 8 thin large Arial 30 125 42 P2 16 thick medium Fancy 20 126 42 P3 8 thick large Arial 10 127 43 P1 12 none small Times 30 128 43 P2 8 thin small Fancy 20 129 43 P3 12 thin medium Arial 10 130 44 P1 16 none large Fancy 10 131 44 P2 12 thick small Fancy 30 132 44 P3 12 thick medium Arial 30 133 45 P1 12 thin small Arial 30 134 45 P2 8 none large Arial 20 135 45 P3 8 thin small Fancy 20 136 46 P1 8 thin small Fancy 30 137 46 P2 12 thin large Times 30 138 46 P3 12 thick large Fancy 10 139 47 P1 8 thick medium Times 20 140 47 P2 8 none large Fancy 30 141 47 P3 12 thick medium Fancy 20 142 48 P1 8 thick medium Times 20 143 48 P2 16 thin medium Times 10 144 48 P3 16 none large Times 10 145 49 P1 16 thick small Times 20 146 49 P2 12 none small Arial 10 147 49 P3 16 thin medium Fancy 30 148 50 P1 12 thin large Fancy 20 149 50 P2 8 none small Times 10 150 50 P3 8 thick medium Times 10 151 51 P1 12 none medium Arial 30 152 51 P2 16 none medium Times 30 153 51 P3 16 thin medium Fancy 10

font font

Obs Set Product diameter border Size Style price 154 52 P1 16 thick medium Fancy 30 155 52 P2 12 none large Fancy 20 156 52 P3 16 none small Arial 10 157 53 P1 8 none large Times 30 158 53 P2 8 thick large Arial 30 159 53 P3 16 thin large Times 30 160 54 P1 12 thick medium Fancy 20 161 54 P2 16 thick small Arial 30 162 54 P3 12 thin large Arial 10

42

Note: Due to the length of the survey, the complete survey is not included here. The following example demonstrates the layout of the survey. The clock drawings were generated using a Mathematica code.

43

Wall Clock Survey

Thank you for participating in this survey. The following series of questions is about purchases that you may consider making. We are interested in what you personally look for when buying a wall clock for use in your home. The results will help design clocks that better meet customer needs. It does not matter whether you have previously bought a wall clock for your home or if you are currently considering buying one. For the purposes of the survey, we ask you to imagine that you are currently in the market for a wall clock for your home and ask that your choices reflect your preferences accordingly. Please also imagine that it’s not absolutely necessary to purchase one. The survey is printed on the front and back of each page. The survey begins with four brief questions that will help in analyzing the data. The personal information will remain strictly confidential and is for statistical purposes only. You then be presented with 54 clock choices. On each page there will be three clocks from to choose from. Please select the clock that appeals the most to you by checking the box next to “Clock 1,” “Clock 2,” or “Clock 3.” If none of the clocks appeal to you, select the box at the bottom next to the last choice: “I would NOT purchase any of these clocks.” Please make a selection on each of the 54 pages and please make each choice according to your preference, not by selecting randomly. Assume each of the clocks has a Quartz movement and has an adhesive wall hanger that won’t damage your wall. Please also assume that the clock is mostly constructed of plastic, has an on/off switch, and takes 1 AA battery. Each clock will be pictured and will have a brief description consisting of face diameter (excluding frame), total diameter (including frame), and price. Several elements will vary from one clock to the next and you should not assume that any clock is ‘necessarily better’ than another—all that is important is that you select the clock that you believe suits your needs and tastes most closely, if at all. If you have questions about the survey, email Kristi Schmidt (krischmi@umich.edu) or Ilkin Hossoy (ihossoy@umich.edu). Before beginning the survey, please answer a few brief questions about yourself: Gender: MALE FEMALE Age: ____________________ Do you need vision correction to see clearly at a distance of 20 feet (~6 meters)? YES NO Have you purchased a wall clock for your home in the past two years? YES NO

44

Clock 1 ٱ Clock 2 ٱ Clock 3 ٱ

12111098

7 6 543

21

121110987 6 54

321 1211

1098

7 6 543

21

Face diameter Total diameter Price

12” (30.5 cm) 13 ⅛” (33.3 cm) $10

Face diameter Total diameter Price

12” (30.5 cm) 14 ¼” (36.2 cm) $20

Face diameter Total diameter Price

16” (40.6 cm) 19” (48.3 cm) $10

I would NOT purchase any of these clocks. ٱ

Clock 1 ٱ Clock 2 ٱ Clock 3 ٱ

45

1211

10

9

8

76

5

4

3

2

1

12111098

7 6 543

21

121110

9

87 6 5

4

3

21

Face diameter Total diameter Price

12” (30.5 cm) 14 ¼” (36.2 cm) $10

Face diameter Total diameter Price

16” (40.6 cm) 19” (48.3 cm) $20

Face diameter Total diameter Price

12” (30.5 cm) 14 ¼” (36.2 cm) $30

I would NOT purchase any of these clocks. ٱ

46

47

APPENDIX 2: SAS CODE FOR SURVEY DESIGN %include 'H:\Private\SAS MACROS\mktallo.sas'; %include 'H:\Private\SAS MACROS\mktbal.sas'; %include 'H:\Private\SAS MACROS\mktblock.sas'; %include 'H:\Private\SAS MACROS\mktdes.sas'; %include 'H:\Private\SAS MACROS\mktdups.sas'; %include 'H:\Private\SAS MACROS\mkteval.sas'; %include 'H:\Private\SAS MACROS\mktex.sas'; %include 'H:\Private\SAS MACROS\mktkey.sas'; %include 'H:\Private\SAS MACROS\mktlab.sas'; %include 'H:\Private\SAS MACROS\mktmerge.sas'; %include 'H:\Private\SAS MACROS\mktorth.sas'; %include 'H:\Private\SAS MACROS\mktroll.sas'; %include 'H:\Private\SAS MACROS\mktruns.sas'; %include 'H:\Private\SAS MACROS\choiceff.sas'; %include 'H:\Private\SAS MACROS\phchoice.sas'; %include 'H:\Private\SAS MACROS\plotit.sas'; %mktruns(3 3 3 3 3 3 3 3 3 3 3 3 3 3 3); %let m=4; %let mm1=%eval(&m-1); %let n=54; %mktex(3 3 3 3 3 3 3 3 3 3 3 3 3 3 3,n=54); proc format; value diameter 1='8' 2='12' 3='16'; value border 1='none' 2='thin' 3='thick'; value fontSize 1='small' 2='medium' 3='large'; value fontStyle 1='Times' 2='Arial' 3='Fancy'; value price 1='10' 2='20' 3='30'; run; %mktlab(data=randomized, vars=x1-x15, out=sasuser.des) %mkteval(data=design, print=freqs); proc data=sasuser.des; run; options ls=80 ps=60 nonumber nodate; data _null_; array alternatives[&mm1] $ 10 _temporary_ ('alter.1 ' 'alter.2 ' 'alter.3 '); array diameter[3] $10 _temporary_ ('8' '12' '16'); array border[3] $13 _temporary_ ('none' 'thin' 'thick'); array fontSize[3] $10 _temporary_ ('small' 'medium' 'large'); array fontStyle[3] $10 _temporary_ ('Times' 'Arial' 'Fancy'); array price[3] $10 _temporary_ ('10' '20' '30'); array x[15]; file print linesleft=ll; set sasuser.des; put _page_; put @50 'Form: ' ' Subject: -------'//; if ll<51 then put _page_; put _n_ 2. ') Circle your choice of alternative :'; do pi = 1 to &mm1; put ' ' pi 1. ') ' alternatives[pi] +(-1) ' price:' price[x[pi]] +(-1) ', with diameter:' diameter[x[&mm1+pi]] +(-1) ' border: ' border[x[2*&mm1+pi]] +(-1) '.'; end; put " &m) none"/; run;

48

data key; input Product $ diameter $ border $ fontSize $ fontStyle $ price $ ; datalines; P1 x1 x4 x7 x10 x13 P2 x2 x5 x8 x11 x14 P3 x3 x6 x9 x12 x15 None . . . ; proc print; run; %mktroll(design=randomized,key=key,alt=product, out=rolled); proc print data=rolled; format diameter diameter. border border. fontSize fontSize. fontStyle fontStyle. price price. ; run;

APPENDIX 3: RAW SURVEY DATA

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 361 1 1 1 1 4 1 1 2 3 1 3 1 1 1 1 1 1 1 3 1 1 3 1 3 3 1 1 1 3 1 1 1 1 3 12 1 2 4 1 2 2 1 2 2 1 1 4 1 1 1 4 1 4 2 2 4 2 2 4 2 2 2 1 2 1 4 4 1 2 23 3 3 4 2 1 2 3 1 3 4 2 4 3 3 3 2 3 4 2 3 4 4 4 4 2 3 2 1 4 2 4 3 4 2 34 2 2 4 2 3 2 2 2 2 2 2 2 2 2 2 4 3 4 1 4 2 4 4 1 2 2 2 4 2 1 4 1 4 2 25 1 1 4 1 1 1 1 1 1 4 4 1 1 1 1 3 1 4 3 4 4 4 4 4 4 1 1 4 4 4 4 3 4 2 16 2 1 4 1 2 3 1 3 4 4 4 1 4 1 2 1 4 2 3 4 4 4 4 2 4 2 4 3 4 4 2 4 2 47 4 1 4 3 4 3 4 3 3 4 4 2 4 2 2 3 4 1 4 4 4 4 4 2 1 4 1 4 4 4 1 4 4 48 2 4 2 3 1 1 4 4 1 4 2 4 2 1 2 4 1 4 2 1 4 4 1 4 3 3 4 1 4 4 4 2 1 3 49 2 1 3 2 2 1 4 4 1 1 3 4 1 1 1 2 1 4 3 1 4 4 4 1 1 1 2 1 1 1 4 3 4 3 410 3 3 4 1 3 2 4 2 2 3 3 3 3 3 3 4 1 3 4 3 4 4 4 4 4 4 4 4 4 4 2 1 3 3 411 1 1 4 2 2 2 2 4 4 4 1 2 1 2 1 1 2 4 1 4 4 4 4 1 1 1 1 2 1 1 4 2 2 1 412 3 1 4 1 3 1 1 4 4 3 3 4 3 1 1 3 1 4 3 4 1 4 4 3 3 4 3 4 3 3 4 1 4 2 413 1 4 4 3 2 3 4 3 3 4 1 4 1 3 2 1 3 4 1 3 4 4 4 1 1 2 1 2 4 1 4 1 4 1 414 1 1 4 2 4 3 4 2 2 1 4 4 1 1 1 4 3 4 1 3 4 4 4 1 3 3 1 4 3 1 4 4 4 1 415 1 1 4 1 4 1 3 4 4 1 1 1 1 1 1 4 3 1 1 3 1 3 3 4 4 3 4 2 1 3 3 2 3 416 1 1 4 1 4 1 1 4 1 1 2 4 1 1 2 2 1 1 2 4 4 1 1 1 1 1 2 4 4 1 1 2 1 2 117 4 4 4 3 4 1 2 1 4 4 2 4 1 2 1 4 4 1 4 1 1 4 4 1 4 4 1 4 1 4 3 1 118 2 3 4 3 4 2 2 2 2 4 4 3 2 2 2 4 2 2 2 2 4 4 4 2 2 2 2 4 1 2 4 3 4 1 219 3 3 4 3 4 3 3 3 3 3 3 3 3 3 1 3 3 3 3 3 3 4 4 3 3 3 3 2 3 3 4 4 4 1 420 1 1 4 3 4 3 4 4 1 4 4 4 4 2 4 3 4 4 1 4 1 1 4 1 4 1 3 1 4 1 4 1 2 121 2 2 4 1 4 1 4 3 1 2 2 4 2 4 1 3 1 4 4 4 4 1 1 4 2 4 2 1 4 2 4 4 1 2 422 1 1 4 3 4 2 4 2 2 4 1 4 1 1 1 2 2 4 1 4 4 4 4 2 4 4 2 4 4 4 4 2 4 4 423 2 2 4 2 4 2 2 4 2 4 4 2 2 2 2 2 2 4 4 2 4 2 2 4 2 2 2 2 3 4 4 2 2 2 424 3 4 2 4 1 4 4 3 4 4 1 3 2 1 1 3 4 4 3 4 4 4 3 3 3 4 3 4 4 1 3 2 425 2 2 3 4 4 1 4 2 2 2 2 2 2 2 2 2 2 2 3 2 3 2 2 2 2 2 2 4 2 2 2 2 2 126 2 4 4 2 4 3 3 2 2 4 2 4 2 4 2 2 2 4 2 3 4 4 4 4 2 4 2 3 2 2 4 2 4 2 227 1 1 1 1 4 3 1 4 1 1 1 1 1 1 1 2 1 1 1 1 4 1 1 1 1 1 1 1 1 1 1 1 1 1 128 2 3 4 3 4 2 4 3 1 4 4 2 4 2 2 2 4 4 2 4 2 2 4 4 2 4 2 2 4 4 4 2 4 429 3 4 4 2 4 2 4 4 4 4 3 4 3 4 3 2 1 4 4 1 3 4 4 4 4 4 4 4 4 4 4 3 2 1 430 1 2 4 1 4 2 4 4 1 2 2 4 1 4 2 4 2 4 2 4 4 4 4 2 1 4 1 4 1 1 4 4 4 1 431 3 4 1 3 4 2 3 4 3 4 4 4 3 4 1 4 3 4 4 4 4 4 4 4 3 3 3 4 3 3 4 1 4 3 432 2 2 1 3 4 2 2 4 2 2 4 4 2 4 2 4 2 4 1 4 4 4 4 2 2 2 2 4 4 2 4 1 4 1 433 1 3 4 3 4 1 3 1 2 3 3 3 1 2 3 1 2 2 1 2 3 2 2 1 2 2 1 2 2 1 2 3 3 2 234 3 3 4 2 4 1 4 3 4 1 1 4 3 1 3 3 2 4 3 4 4 4 4 3 3 1 3 4 4 3 4 2 1 1 435 2 2 2 2 3 3 2 4 2 2 2 2 2 2 1 1 1 2 1 4 2 2 4 2 4 2 1 2 4 4 2 2 2 1 236 2 2 4 2 2 3 2 2 3 2 2 2 2 2 2 2 2 4 2 3 2 3 4 2 4 3 4 3 3 4 4 2 3 4 337 1 1 4 1 2 1 4 4 3 1 1 4 1 1 1 2 1 4 4 3 4 3 3 4 4 3 4 3 3 4 4 4 3 1 338 2 2 4 3 1 2 4 1 1 2 4 4 2 2 1 1 2 2 2 4 4 3 4 2 2 1 2 2 2 2 4 2 3 2 139 2 2 2 2 4 2 4 4 4 4 4 4 2 2 2 2 2 4 2 4 4 4 4 2 1 4 2 2 2 4 4 2 4 1 440 3 3 3 3 4 3 3 1 1 2 3 1 3 3 3 1 1 4 4 1 3 4 4 2 3 1 3 3 1 1 4 3 3 3 341 3 2 4 2 2 2 4 1 1 4 4 4 2 2 2 3 3 4 3 1 4 2 2 2 1 2 4 4 4 4 3 2 3 142 3 3 4 2 1 1 4 4 4 4 3 4 3 4 3 4 3 4 4 4 4 4 4 3 2 4 3 2 4 4 4 4 2 443 3 3 3 1 4 1 3 1 3 3 3 3 3 3 3 1 3 3 3 3 4 3 3 3 3 3 3 3 3 3 4 3 3 3 344 1 4 4 2 4 3 4 4 3 4 4 4 1 4 1 1 3 4 1 3 4 4 4 1 1 3 3 4 1 1 4 4 3 3 345 3 2 4 1 4 3 4 4 1 4 4 4 1 4 2 2 1 4 2 1 4 1 4 4 4 1 4 1 4 4 4 3 1 4 446 3 4 4 1 2 2 3 4 2 4 3 4 3 4 3 4 2 4 3 4 4 4 4 3 3 4 3 2 2 3 4 4 4 3 447 4 1 4 1 1 1 4 4 1 4 4 4 3 1 1 2 1 4 4 4 4 1 4 3 1 3 4 4 4 4 4 1 4 448 2 3 4 1 4 2 2 3 2 2 4 4 2 2 3 3 2 2 3 2 2 2 2 3 2 2 2 2 2 3 4 4 2 2 249 2 2 4 2 4 2 2 2 1 2 2 2 2 2 2 3 2 4 2 4 2 4 4 4 1 2 2 4 4 2 4 2 1 1 250 2 2 1 2 1 2 3 4 4 3 3 4 2 2 2 1 3 4 1 4 2 4 4 3 1 3 1 4 1 3 2 3 1 351 3 4 4 2 2 2 3 1 2 4 4 4 3 4 3 3 1 4 3 4 4 4 4 3 3 2 3 4 3 3 4 3 4 3 452 3 3 4 3 4 3 3 3 3 3 4 4 3 3 3 2 3 4 2 3 3 4 4 3 3 3 3 4 1 3 4 3 4 4 353 4 4 4 4 4 1 4 4 3 4 4 4 3 4 3 3 3 4 4 4 4 3 4 4 4 4 3 4 4 4 4 4 4 454 3 3 4 2 4 2 4 4 2 3 3 4 3 4 3 4 1 4 3 2 4 1 4 3 1 4 3 4 2 3 4 2 1 4

QU

ESTI

ON

#

SUBJECT #

49

APPENDIX 4: DENDROGRAM FROM SPSS HIERARCHICAL CLUSTER ANALYSIS

50

APPENDIX 5: DEMAND CURVES FOR THREE MARKET SEGMENTS

-1.6-1.4-1.2-1.0-0.8-0.6-0.4-0.20.00.20.40.60.81.01.21.41.6

8 12 16

diameter (in.)

Bet

a1

Figure 12: Segment 1 face diameter demand curve

-1.6-1.4-1.2-1.0-0.8-0.6-0.4-0.20.00.20.40.60.81.01.21.41.6

1 2 3

border (none, thin, thick)

Bet

a2

Figure 13: Segment 1 frame thickness demand curve

-1.6-1.4-1.2-1.0-0.8-0.6-0.4-0.20.00.20.40.60.81.01.21.41.6

1 2 3

font size (small, medium, large)

Bet

a3

Figure 14: Segment 1 font size demand curve

-1.6-1.4-1.2-1.0-0.8-0.6-0.4-0.20.00.20.40.60.81.01.21.41.6

10 20 30

price ($)

Bet

a5

Figure 15: Segment 1 price demand curve

-1.6-1.4-1.2-1.0-0.8-0.6-0.4-0.20.00.20.40.60.81.01.21.41.6

1 2

font style (Times N. R., Arial, Adolescene)

Bet

a4

3

Figure 16: Segment 1 font style demand

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-2.2-2.0-1.8-1.6-1.4-1.2-1.0-0.8-0.6-0.4-0.20.00.20.40.6

8 12 16

diameter (in.)

Bet

a1

Figure 17: Segment 2 face diameter demand curve

-2.2-2.0-1.8-1.6-1.4-1.2-1.0-0.8-0.6-0.4-0.20.00.20.40.6

1 2 3

border (none, thin, thick)

Bet

a2

Figure 18: Segment 2 frame thickness demand curve

-2.2-2.0-1.8-1.6-1.4-1.2-1.0-0.8-0.6-0.4-0.20.00.20.40.6

1 2 3

font size (small, medium, large)

Bet

a3

Figure 19: Segment 2 font size demand curve

-2.2-2.0-1.8-1.6-1.4-1.2-1.0-0.8-0.6-0.4-0.20.00.20.40.6

10 20 30

price ($)

Bet

a5

Figure 20: Segment 2 price demand curve

-2.2-2.0-1.8-1.6-1.4-1.2-1.0-0.8-0.6-0.4-0.20.00.20.40.6

1 2

font style (Times N. R., Arial, Adolescene)

Bet

a4

3

Figure 21: Segment 2 font style demand

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-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

8 12 16

diameter (in.)

Bet

a1

Figure 22: Segment 3 face diameter demand curve

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

1 2 3

border (none, thin, thick)

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a2

Figure 23: Segment 3 frame thickness demand curve

-1.2

-1.0

-0.8

-0.6

-0.4

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0.0

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font size (small, medium, large)

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a3

Figure 24: Segment 3 font size demand curve

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

10 20 30

price ($)

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a5

Figure 25: Segment 3 price demand curve

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

1 2

font style (Times N. R., Arial, Adolescene)

Bet

a4

3

Figure 26: Segment 3 font style demand

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APPENDIX 6 : BUSINESS PLAN

I. Business Opportunity

1. Business objective KIlock is a start-up clock producer and distribution company. Its strategy is to serve the midrange residential markets of the wall clock industry with a new product that has an adhesive hanger. KIlock is a privately-held corporation with sales and marketing focused on the United States for the short-term future. KIlock’s long term goal is to achieve a 10% market share in the United States, build brand image and brand equity through marketing, and eventually produce luxury adhesive wall clocks in addition to the initial, moderately-priced line.

2. Product description The KIlock is a quartz wall clock with adhesive hanger that is economical as well as functional and particular attention has been paid to size, weight, and appearance with respect to functionality and cost. The clock has an adhesive hanger that makes it possible to hang on a wall without needing to drill a hole. Additionally, the adhesive hanger is reliable and will not leave a mark on the wall upon removal. This gives the user the flexibility to rearrange the room and move the clock. KIlock also has considered ergonomics in the design process. It is readable by a seated average household user with normal or corrected to normal vision in the average living room (average maximum total viewing distance from the user’s eye to the center of the clock is 20.31 feet). The price will be very competitive: approximately $30.

3. Market analysis Its strategy is to serve the midrange residential markets of the wall clock industry with a new product that has an adhesive hanger. There is a market within this industry that desires wall clocks but has not purchased them because they do not want to damage their wall by drilling a hole, in particular those who rent an apartment or home. KIlock’s long term goal is to achieve a 10% market share in the United States. Entry into this market comes at an opportune time, as more and more people are moving from home to home more frequently and also rearrange their rooms following the recent home improvement do-it-yourself boom and do not want to hang a wall clock permanently on their wall. KIlock’s main competitors are Infinity Instruments Ltd., Polder, Bulova, and Timeworks. The intended users for the quartz wall clock with an adhesive hanger are the general population of the United States. The clock is designed for people with a normal or corrected to normal vision for household use. Because households only purchase a new wall clock every 5-10 years, KIlock conservatively assumes that there will be no less than 0.1% of all U.S. households that will purchase a wall clock for their home in a one year span of time. In 2004, the United States Census projects that there will be 107,672,899 households nationwide. Therefore, estimating that 0.1% of all U.S. households will purchase a wall clock for their home sets the KIlock market at 107,672 households. A conjoint analysis and clustering of the market yielded three target markets. The division reflects that differences in marketing strategies and clock face design that will be used to target each market. First is the price sensitive market. They desire a simple yet reliable clock that is “a good deal.” They are not willing to pay extra money for a fancier face or frivolous features.

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Second is the aesthetically sensitive market. They desire an attractive clock and are willing to pay for it to “look good.” Last is the size sensitive market. They are willing to pay more money for a larger clock. Figure 27 illustrates the market segments.

size20%

aesthetics34%

price46%

Figure 27: Market segments

4. Capital and personnel resources The company’s start up costs will be approximately $125,000 ($116,500 initial investment fixed cost plus $8,500 initial inventory and cash). Owners equity will provide $90,000, $15,000 will consist of short-term borrowing, and the rest will be long-term loans. The majority of the start-up costs will consist of product development and design, manufacturing engineering, manufacturing equipment, rent, and initial inventory. Ownership is divided between two principle individuals who are putting up the initial investment. Kristi Schmidt (50% investment) is head of the production department and Ilkin Hossoy (50% investment) is head of the sales and marketing division. The production facility is located in Detroit, Michigan. It is 1,000 square feet and should be large enough for the first three years of the company’s growth. KIlock will be moved to an adjacent 500 square foot warehouse and distributed from this warehouse.

II. Financial Data

1. Capital equipment and supply list KIlock has two plastic injection molding machines as well as assembly line equipment. Lease price for each machine is $1,000 per month and the assembly line is $500 per month. For one year, this lease for two injection molding machines plus the assembly line will cost $30,000. The

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inspection processes is solely done by manpower. A staff engineer will devote 1/12 time to inventory control (annual salary $60,000) by administrating inventory control software that costs $1,000.

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The internal quartz components are purchased from Innovation Specialties, Inc. for $1.50 per quartz movement (includes clock movement with on/off switch and clock hardware). The cost of polyurethane for injection molding is 12.5 cents per cubic inch and the required volume per clock is:

(40)

2 2 2 21 2 2 1

4 5 7 6 2 3( )( )

4 4 4x x x xV x x x x xπ π π π−

= × × + + × × + × × + × × × 6x x

Tool cost for all manufacturing processes is based upon the injection molding and assembly. Injection molding offers high production rates but the tooling is costly. We estimate that each tool costs $500 but on average will produce 1,000 parts. Per clock, this averages 50 cents. A worker that gets paid $10/hour places a AA battery into the clock, tests that it runs and also inspects the clock for manufacturing defects. This process takes the worker on average 1 minute per clock including transition time. This equates to 16 cents per clock.

2. Pro-forma income and cost projections (profit & loss statements) KIlock assumes that market share will increase over time and then level off at 10% by the end of the third year as illustrated in Figure 28. Using this market share, net sales, total cost, and gross margin can be obtained. Gross margin is total sales minus total cost. Net profit is defined as net sales minus taxes, interest, depreciation, and other expenses. Further analysis must be done to estimate taxes, interest, depreciation, and other expenses. Figure 29 illustrates the net sales and gross margin over a three year period of time.

0

1

2

3

4

5

6

7

8

9

10

0 1 2 3

time (years)

mar

ket s

hare

(% to

tal)

Figure 28: Expected market share over time

-150000

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0

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mon

ey ($

)Net salesGross margin

Figure 29: Net sales and Gross margin over time

4. Three-year summary The three-year summary considers the gross margin (total sales minus total cost) over the three year period, starting at time 0 when the initial investment of $125,000 is made ($116,500 fixed cost for the first year of production plus $8,500 cash and material costs). The present value of the gross margins at time zero, year one, year two, and year three is -$59,595.4. This product should not be invested in under these conditions.

3. Breakeven analysis The breakeven analysis, as the three-year summary, shows in Figure 30 that KIlock should not invest under the current conditions laid out in this business plan. There is no breakeven point within the first three years of production and sale. This is a bad indicator in the clock market, particularly since KIlock assumes that demand will level off after three years at 10%.

-150000

-100000

-50000

0

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0 1 2 3

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ey ($

)

KIlock6% Investment

Figure 30: Breakeven analysis

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5. Assumptions upon which projections were based KIlock assumes that the quantity of wall clocks produced equals the quantity sold. It is also assumed that KIlock is initially involved in all aspects of the manufacturing and sales. For example, KIlock may be sold directly as an online merchant of amazon.com rather than in retail stores. A shipment cost of $3.34/clock was considered in the cost model and reflects a free shipping option to consumers. KIlock assumes that the adhesive hanger quartz wall clock will be a novel and appealing product and will then have an increasing market share, but will eventually level off.

III. Supporting Documents

1. Existing patents A United States patent search was conducted using the United States Patent and Trademark Office online database. The database searches from 1790 to present and our search terms were “TTL/quartz” AND “clock.” The search returned 52 patents, but only 17 were relevant to KIlock. These 17 patents were reviewed and are summarized in Table 1. Note that there are no quartz wall clocks with adhesive hanger patents. A KIlock lawyer is currently submitting a patent form to the U.S. patent office.

Table 8: Summary of U.S. patent search of similar products

Pat. No. 3,939,644 – Circuit arrangement for controlling the running of a quartz-controlled electric clock Pat. No. 3,943,695 – Quartz crystal controlled timekeeping apparatus Pat. No. 3,945,194 – Electronic quartz clock with integrated circuits Pat. No. 3,973,148 – Quartz crystal vibrator unit Pat. No. 4,037,402 – Circuit arrangement for a quartz controlled electrical clock Pat. No. 4,087,957 – Movement construction for small size analog quartz timepiece Pat. No. 4,173,863 – Analog quartz timepiece Pat. No. 4,176,515 – Electronic clock, particularly a quartz clock Pat. No. 4,261,048 – Analog quartz timepiece Pat. No. 4,364,673 – Electric clock, particularly a quartz clock Pat. No. 4,367,956 – Clockwork of an electric quartz clock Pat. No. 4,417,820 – Time-keeping device, especially a quartz-controlled clock Pat. No. 4,445,785 – Electronic time setting for a quartz analog watch Pat. No. 4,508,458 – Electric clock movement, particularly a quartz clock movement Pat. No. D302,137 – Quartz clock movement Pat. No. D358,994 – Quartz clock with wildlife picture Pat. No. 6,359,840 – Microcontroller regulated quartz clock

2. Technical analysis and benchmarking The benchmarking process measures competitor’s products according to specified standards in order to compare it with and improve the KIlock product. Currently, KIlock has conducted only competitive analysis online, so actual measurements have not been conducted. Information obtained online is the extent of the technical analysis and benchmarking process thus far. The following represents the current extent of technical analysis and benchmarking:

Three online merchants—Amazon [http://www.amazon.com; Home & Garden>Furniture & Décor>Home Décor>Clocks>Wall Clocks], Clocko [http://www.clocko.com], and TopClock.com [http://www.topclock.com] have a wide selection of wall clock products representative of KIlock’s major competitors. We limit discussion of competitive products to battery operated quartz wall clocks. The following is a discussion of a typical clock produced by each of several competitors. Infinity Instruments Ltd.: According to their website, “Infinity Instruments fuses design innovation and quality to create contemporary, functional accessories to decorate and enrich the home. Infinity sells to the trade only.” This $29.99 metal clock measures 9.5” in diameter and 2.75” thick with no second hand. This clock has tickmarks and retro aesthetic appeal. Polder: Polder sells clocks on their webpage as well as to registered vendors. This $17.99 silver-toned plastic clock measures 10” in diameter and 1.5” thick with a second hand. It weights 2 pounds and requires 1 AA battery. The face is glass crystal, has excellent legibility (although small numbers) and tickmarks, and has contemporary aesthetic appeal. Bulova [http://bulova.com]: Founded in 1875, The Bulova Corporation is headquartered in New York and is part of the American-owned and operated Loews Corporation. This $29.50 “country casual” wall clock measures 10” in diameter and 1.5” thick. There is a wide metal frame, protective glass lens, verdigris finish, Roman numerals, and a second hand. Timeworks: Timeworks was established in 1995 and builds “unique, functional clocks that tell more than just time.” Produced in Berkeley, CA, this $59.99 “Paris Expo” wall clock is 14” in diameter and displays the Eiffel Tower on its face with traditional aesthetics. There is no second hand.

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