EMGT 501 Fall 2005 Midterm Exam Due Day: Oct 17 (Noon)

20
EMGT 501 Fall 2005 Midterm Exam Due Day: Oct 17 (Noon)

Transcript of EMGT 501 Fall 2005 Midterm Exam Due Day: Oct 17 (Noon)

Page 1: EMGT 501 Fall 2005 Midterm Exam Due Day: Oct 17 (Noon)

EMGT 501

Fall 2005

Midterm Exam

Due Day: Oct 17 (Noon)

Page 2: EMGT 501 Fall 2005 Midterm Exam Due Day: Oct 17 (Noon)

Note:

(a) Do not send me after copying your computer results of QSB. Answer what are your decision variables, formulation and solution, only. See my HW answer on my HP.

(b) Put your mailing address so that I will be able to return your exam result via US postal service.

(c) Answer on a PPS series of slides.

(d) Do not discuss on the exam with other students.

(e) Return your answer attached to your e-mail.

Page 3: EMGT 501 Fall 2005 Midterm Exam Due Day: Oct 17 (Noon)

1. Linear Programming (20%)Benson Electronics manufactures three components to produce cellular telephones and other communication devices. In a given production period, demand for the three components may exceed Benson’s manufacturing capacity. In this case, the company meets demand by purchasing the components from another manufacturer at an increased cost per unit. Benson’s manufacturing cost per unit and purchasing cost per unit for the three components are as follows:

Source Component 1 Component 2 Component 3Manufacture $4.50 $5.00 $2.75Purchase $6.50 $8.80 $7.00

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Manufacturing times in minutes for Benson’s three departments are as follows:

Department Component 1 Component 2 Component 3Production 2 3 4Assembly 1 1.5 3Testing and packaging 1.5 2 5

For instance, each unit of component 1 that Benson manufactures requires 2 minutes of production time, 1 minute of assembly time, and 1.5 minutes of testing and packaging time. For the next production period, Benson has capacities of 360 hours in the production department, 250 hours in the assembly department, and 300 hours in the testing and packaging department.

Page 5: EMGT 501 Fall 2005 Midterm Exam Due Day: Oct 17 (Noon)

a. Formulate a linear programming model that can be used to determine how many units of each component to manufacture and how many units of each component to purchase. Assume that component demands that must be satisfied are 6000 units for component 1, 4000 units for component 2, and 3500 units for component 3. The objective is to minimize the total manufacturing and purchasing costs.

b. What is the optimal solution? How many units of each component should be manufactured and how many units of each component should be purchased?

c. Show its dual formulation d. Discuss complementary slackness condition between the

primal and dual models.

Page 6: EMGT 501 Fall 2005 Midterm Exam Due Day: Oct 17 (Noon)

2. Linear Programming (15%)Consider the following problem.

Maximize ,234 4321 xxxxZ

subject to 423

524

4321

4321

xxxx

xxxx

.0,0,0,0 4321 xxxx

Page 7: EMGT 501 Fall 2005 Midterm Exam Due Day: Oct 17 (Noon)

(a) Solve the problem.

(b) What is B-1? How about B-1b and CBB-1b?

(c) If the right hand side is changed from (5, 4) to (6, 5), how is an optimal solution changed? How about an optimal objective value?

Page 8: EMGT 501 Fall 2005 Midterm Exam Due Day: Oct 17 (Noon)

3. Linear Programming (15%)Suppose that in a product-mix problem x1, x2, x3,and x4 indicate the units of products 1,2,3, and 4, respectively, and we have

Max ,1364 4321 xxxx

s.t.

2002132

7001214

5503425.1

4321

4321

4321

xxxx

xxxx

xxxx

0,,, 4321 xxxx

Machine A hours

Machine B hours

Machine C hours

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a. Formulate the dual model to this problem.b. Solve the dual. Use the dual solution to show that the

profit-maximizing product mix is x1=0, x2=25, x3=125, and x4=0.

c. Use the dual variables to identify the machine or machines that are producing at maximum capacity. If the manager can select one machine for additional production capacity, which machine should have priority? Why?

Page 10: EMGT 501 Fall 2005 Midterm Exam Due Day: Oct 17 (Noon)

4. PERT/CPM (20%)Building a backyard swimming pool consists of nine major activities. The activities and their immediate predecessors are shown. Develop the project network.

Activity A B C D E F G H I

ImmediatePredecessor - - A,B A,B B C D D,F E,G,H

Assume that the activity time estimates (in days) for the swimming pool construction project are as follows:

Page 11: EMGT 501 Fall 2005 Midterm Exam Due Day: Oct 17 (Noon)

Activity

ABCDEFGHI

Optimistic

325721563

Most Probable

546942884

Pessimistic

667

1063

1010

5

a. What is an activity schedule?b. What is a critical path?c. What is the expected time to complete the project?d. What is the probability that the project can be completed in

25 or fewer days?

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5. Inventory (15%)

Wilson Publishing Company produces books for the retail market. Demand for a current book is expected to occur at a constant annual rate of 7200 copies. The cost of one copy of the book is $14.50. The holding cost is based on an 18% annual rate, and production setup costs are $150 per setup. The equipment on which the book is produced has an annual production volume of 25,000 copies. Wilson has 250 working days per year, and the lead time for a production run is 15days. Use the production lot size model to compute the following values:

Page 13: EMGT 501 Fall 2005 Midterm Exam Due Day: Oct 17 (Noon)

a. Minimum cost production lot sizeb. Number of production runs per yearc. Cycle timed. Length of a production rune. Maximum inventoryf. Total annual costg. Reorder point

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6. Inventory (15%)A well-known manufacturer of several brands of toothpaste uses the production lot size model to determine production quantities for its various products. The product known as Extra White is currently being produced in production lot sizes of 5000 units. The length of the production run for this quantity is 10 days. Because of a recent shortage of a particular raw material, the supplier of the material announced that a cost increase will be passed along to the manufacturer of Extra White. Current estimates are that the new raw material cost will increase the manufacturing cost of the toothpaste products by 23% per unit. What will be the effect of this price increase on the production lot sizes for Extra White?

Page 15: EMGT 501 Fall 2005 Midterm Exam Due Day: Oct 17 (Noon)

EMGT 501

HW #4

SolutionsChapter 11 - SELF TEST 3

Chapter 11 - SELF TEST 7

Chapter 11 - SELF TEST 17

Page 16: EMGT 501 Fall 2005 Midterm Exam Due Day: Oct 17 (Noon)

Ch. 11 – 3

* 2 2(5000)(32)400

2O

h

DCQ

C

5000 20 units per day

250 250

Dd

a. r = dm = 20(5) = 100Since , both inventory position and inventory on hand equal 100.

b. r = dm = 20(15) = 300Since , both inventory position and inventory on hand equal 300.

*Qr

*Qr

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c. r = dm = 20(25) = 500Inventory position reorder point = 500. One order of Q* = 400 is outstanding. The on-hand inventory reorder point is 500 - 400 = 100.

d. r = dm = 20(45) = 900Inventory position reorder point = 900. Two orders of Q* = 400 are outstanding. The on-hand inventory reorder point is 900 - 2(400) = 100.

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* 2 2o o

h

DC DCQ

C IC

2'

'oDC

QI C

Where is the revised order quantity for the new carrying charge . Thus

'Q'I

*

*

2 / ''/

'2 /

''

0.22' (80) 72

0.27

o

o

DC I C IQ Q

IDC IC

IQ Q

I

Q

Ch. 11 – 7

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Ch. 11 – 17

EOQ Model

2 2(800)(150)* 282.84

3o

h

DCQ

C

Total Cost

0

1 282.84 8003 (150) $848.53

2 2 282.84h

DQC C

Q

Planned Shortage Model

2 2(800)(150) 3 20* 303.32

3 20o h b

h b

DC C CQ

C C

Page 20: EMGT 501 Fall 2005 Midterm Exam Due Day: Oct 17 (Noon)

3* * 303.32 39.56

3 20h

h b

CS Q

C C

Total Cost2 2( )

344.02 395.63 51.60 $791.252 2h o b

Q S D SC C C

Q Q Q

Cost Reduction with Backorders allowed$848.53 - 791.25 = $57.28 (6.75%)

Both constraints are satisfied:1. S / Q = 39.56 / 303.32 = 0.13Only 13% of units will be backordered.2. Length of backorder period = S / d = 39.56 / (800/250)

= 12.4 days