ADVANCED MANAGEMENT

SCIENCE

PROJECT ON ANALYTICAL

HEIRARCHY PROCESS AND

FABRICS AND FALL FASHION

Submitted to: DR. G.N. Patel

Submitted by: UDIT JAIN

13DM206

INTRODUCTION

Analytical heirarchy process is a structured technique for organizing and analysing complex

decisions, based on mathematics and psychology. It is designed for situations in which ideas,

feelings, and emotions affecting the decision process are quantified to provide a numeric

scale for prioritizing the alternatives. Decision Making involves setting priorities and the

AHP is the methodology for doing that.

Rather than prescribing a "correct" decision, the AHP helps decision makers find one that

best suits their goal and their understanding of the problem. It provides a comprehensive and

rational framework for structuring a decision problem, for representing and quantifying its

elements, for relating those elements to overall goals, and for evaluating alternative solutions.

Users of the AHP first decompose their decision problem into a hierarchy of more easily

comprehended sub-problems, each of which can be analyzed independently. The elements of

the hierarchy can relate to any aspect of the decision problem—tangible or intangible,

carefully measured or roughly estimated, well or poorly understood—anything at all that

applies to the decision at hand.

Once the hierarchy is built, the decision makers systematically evaluate its various elements

by comparing them to one another two at a time, with respect to their impact on an element

above them in the hierarchy. In making the comparisons, the decision makers can use

concrete data about the elements, but they typically use their judgments about the elements'

relative meaning and importance. It is the essence of the AHP that human judgments, and not

just the underlying information, can be used in performing the evaluations.

The AHP converts these evaluations to numerical values that can be processed and compared

over the entire range of the problem. A numerical weight or priority is derived for each

element of the hierarchy, allowing diverse and often incommensurable elements to be

compared to one another in a rational and consistent way. This capability distinguishes the

AHP from other decision making techniques.

In the final step of the process, numerical priorities are calculated for each of the decision

alternatives. These numbers represent the alternatives' relative ability to achieve the decision

goal, so they allow a straightforward consideration of the various courses of action.

USES AND APPLICATION

The Analytic Hierarchy Process (AHP) is most useful where teams of people are working on

complex problems, especially those with high stakes, involving human perceptions and

judgments, whose resolutions have long-term repercussions.[3] It has unique advantages

when important elements of the decision are difficult to quantify or compare, or where

communication among team members is impeded by their different specializations,

terminologies, or perspectives.

Decision situations to which the AHP can be applied include:

Choice – The selection of one alternative from a given set of alternatives, usually

where there are multiple decision criteria involved.

Ranking – Putting a set of alternatives in order from most to least desirable

Prioritization – Determining the relative merit of members of a set of alternatives, as

opposed to selecting a single one or merely ranking them

Resource allocation – Apportioning resources among a set of alternatives

Benchmarking – Comparing the processes in one's own organization with those of

other best-of-breed organizations

Quality management – Dealing with the multidimensional aspects of quality and

quality improvement

Conflict resolution – Settling disputes between parties with apparently incompatible

goals or positions

RANKING OF SONGS

In our case we have to rank the selected songs according to our preferences.

Objective : Choose the best song among the selected five

Criteria:

Alternatives:

Since five criteria (N) have been chosen for selecting the best song hence there will be six

(N+1) pairwise matrix comparisons. The following are the six matrices:

Pairwise comparison of criteria (Cr)

Pairwise comparison of songs for Lyrics (Lr)

Pairwise comparison of songs for Music (M)

Pairwise comparison of songs for Singer (S)

Pairwise comparison of songs for Location (L)

Pairwise comparison of songs for Actor (A)

In order to find out the best song analytical hierarchy process has been used. The three main

methods used for decision making i.e finding out the weights are:

Eigen value method

Iteration method

Lyrics

Music

Singer

Location

Actor

O hasina zulfo wali ohz

Chup gaye sare nazare cgs

Malish tel malish mtm

ude jab jab zulfe ujj

Aaj mausamb bada amb

Linear programming method

The scale used for pairwise comparison is a nine point scale the detail of which is as follows:

1 Equally preferred

2 Equally to Moderately preferred

3 Moderately preferred

4 Moderately to Strongly preferred

5 Strongly preferred

6 Strongly to Very Strongly preferred

7 Very Strongly preferred

8 Very strongly to Extremely preferred

9 Extremely preferred

METHODOLOGY

1. HEIRARCHICAL DECOMPOSITION

Best Song

Lyrics

Ohz hasina julfo

Akhiyo Key jharokhe

sar jab jab

Ude jab jab

Music

Ohz hasina julfho

Akhiyo key jharokhe

Sar jab jab

Ude jab jab

Singer

Ohz hasina julfho

Akhiyo key jharokhe

Sar jab jab

Ude jab jab

Location

Ohz hasina julfho

Akhiyo key jharokhe

Sar jab jab

Ude jab jab

Actor

Ohz hasina julfho

Akhiyo key jharokhe

Sar jab jab

Ude jab jab

2. PAIRWISE MATRIX EVALUATION

Since there are six matrices for which weightage is to be found out hence two matrices have

been solved by using each method. The different methods used for different matrices are –

1. Eigen Value Method

a. Pairwise comparison of criteria (Cr)

b. Pairwise comparison of songs for Location (D)

2. Iteration Method

a. Pairwise comparison of songs for lyrics (L)

b. Pairwise comparison of songs for music (M)

3. Linear Programming Method

a. Pairwise comparison of songs for singer (S)

b. Pairwise comparison of songs for costume (C)

Finally after obtaining the weightages of the criteria matrix and the alternatives for each

criterion, the final rankings of the songs can be found out as follows -

Criteria Weightages Rankings

Songs [ ] × [ ] = [ ]

Let us analyse the six above mentioned matrixes with the help of three methods.

A. Eigen Value Method

Let A = [aij] be the pairwise comparison matrix and w be the Eigen vector i.e. the weights for

each criteria or song. Mostly the consistency of A does not hold for the pairwise comparison

matrices entered by us and hence we find out λmax (slightly greater than n) and find out the

weightages by dividing Axw by λmax.

1. Pairwise comparison of criteria (Cr) by Eigen value method

Lyrics music singer Location actor

Lyrics 1 2 3 5 8

Music 0.50 1 0.20 3 7

Singer 0.33 5 1 8 8

Location 0.20 0.33 0.13 1 3

Actor 0.13 0.14 0.11 0.33 1

Sum 2.158333333 8.47619 4.44 17.33333 27

Normalised matrix Row avg

0.463320463 0.235955 0.67627 0.288462 0.296296 0.39206

0.231660232 0.117978 0.04508 0.173077 0.259259 0.165412

0.154440154 0.589888 0.22542 0.461538 0.296296 0.345517

0.092664093 0.039326 0.02818 0.057692 0.111111 0.065794

0.057915058 0.016854 0.02505 0.019231 0.037037 0.031217

Ranking

2.33814 0.405625

0.846445 0.146843

2.07935 0.360729

0.336183 0.058322

0.164177 0.028482

Nmax 5.764296

2 Pairwise comparison of songs for Lyrics (Lr) by Eigen value method

Ohz cgs mtm ujj amb

Ohz 1 3 2 9 5

Cgs 0.33 1 0.17 4 6

Mtm 0.50 5 1 6 9

Ujj 0.11 0.25 0.17 1 2

Amb 0.11 0.17 0.111111 0.5 1

2.055556 9.416667 3.444444 20.5 23

Normalized

0.486486 0.318584 0.580645 0.439024 0.217391

0.162162 0.106195 0.048387 0.195122 0.26087

0.243243 0.530973 0.290323 0.292683 0.391304

0.054054 0.026549 0.048387 0.04878 0.086957

0.054054 0.017699 0.032258 0.02439 0.043478

Ranking

2.219866 0.412965

0.767011 0.142688

1.95371 0.363452

0.263999 0.049112

0.170843 0.031782

Nmax 5.375429

B. Iteration Method

Let A = [aij] be the pairwise comparison matrix. Calculate A2 and find the row sum. The row

sums are then normalised which forms the weights of the criteria or alternatives. We further

square the obtained pairwise matrix, find the row sum and normalise them to obtain the

weights. We will continue to do this until the weights obtained in two subsequent steps are

similar up to 4 digits (or more if more accuracy is desired). This normalised matrix then

corresponds to the weights of the criteria or the alternatives.

3. Pairwise comparison of songs for Music (M) by iteration method

music

Ohz cgs mtm ujj amb

Ohz 1 3 5 0.142857143 9

Cgs 0.333333333 1 0.125 7 3

Mtm 0.2 8 1 5 6

Ujj 7 0.142857143 0.2 1 4

Amb 0.111111111 0.333333333 0.166666667 0.25 1

A˄2

Row sum

5 49.02040816 11.90357143 48.53571429 57.57142857 172.0311224

50.025 5 3.816666667 15.42261905 37.75 112.0142857

38.73333333 19.31428571 5 67.52857143 57.8 188.3761905

14.53206349 24.21904762 36.08452381 5 72.62857143 152.4642063

2.116666667 2.369047619 0.980555556 3.682539683 5 14.14880952

639.0346145

Normalized

0.2692

0.1753

0.2948

0.2386

0.0221

A˄4

3765.494524 2031.991293 2113.970394 2257.220467 6639.340714 16808.01739

952.1088681 3013.914802 1227.176664 2978.975218 4598.236837 12770.41239

2457.203297 3864.275306 3053.193645 3065.963379 8441.551293 20882.18692

2908.282857 1823.565507 697.4810748 3808.039167 4562.871893 13800.2405

231.1733595 235.5766742 176.9260043 242.3117602 560.4247789 1446.412577

65707.26978

Normalized

0.2558

0.1944

0.3178

0.2100

0.0220

A˄16

Row sum

29407555.25 27624927.5 19657157.79 31238533.11 66209426.71 174137600.4

19196850.7 22276101.63 12349470.37 27348237.01 46708992.15 127879651.9

31302264.34 36017610.7 22890576.31 40139805.63 78577206.36 208927463.3

26530878.31 22120050.47 13978731.62 29742243.29 53514830.49 145886734.2

2363786.238 2437335.442 1586138.771 2824565.151 5531319.432 14743145.03

671574594.8

Normalised

0.2593

0.1904

0.3111

0.2172

0.0220

A˄32

Row sum

2.61738E+12 1.01094E+13 6.04071E+12 1.3543E+12 1.56769E+13 3.57987E+13

5.81986E+11 2.24798E+12 1.34323E+12 3.01139E+11 3.48597E+12 7.96031E+12

1.13809E+12 4.39583E+12 2.62668E+12 5.88869E+11 6.81666E+12 1.55661E+13

5.60297E+12 2.16415E+13 1.29313E+13 2.89922E+12 3.35603E+13 7.66353E+13

3.96977E+11 1.53338E+12 9.16222E+11 2.05412E+11 2.37785E+12 5.42984E+12

1.4139E+14

4. Pairwise comparison of songs for singer (S) by iteration method

singer

ohz cgs mtm ujj Amb

Ohz 1 6 7 0.142857143 6

Cgs 0.166666667 1 0.2 0.25 3

Mtm 0.142857143 5 1 0.125 6

Ujj 7 4 8 1 4

Amb 0.166666667 0.333333333 0.166666667 0.25 1

A˄2

Row sum

5 49.57142857 17.34285714 4.160714286 72.57142857 148.6464286

2.611904762 5 4.066666667 1.298809524 9.2 22.17738095

2.994047619 13.35714286 5 3.020408163 28.35714286 52.7287415

16.47619048 91.33333333 66.46666667 5 110 289.2761905

2.162698413 3.5 3.566666667 0.62797619 5 14.85734127

527.6860828

Normalized

0.2817

0.0420

0.0999

0.5482

0.0282

A˄4

Row sum

431.9040249 1361.377211 910.4059524 203.9466229 2131.243878 5038.877689

79.59109977 359.6195011 205.1054308 41.91585884 539.7377551 1225.969646

175.9208293 657.1045918 433.1413265 77.81745323 955.9843537 2299.968555

840.2170635 3002.886395 1714.16644 482.0111678 5020.772109 11060.05317

51.79407596 247.2036848 129.1468537 30.59675454 384.3679705 843.1093396

20467.9784

Normalized

0.2462

0.0599

0.1124

0.5404

0.0412

A˄16

Row sum

736799.2062 2815073.901 1691610.194 379507.8306 4368764.735 9991755.867

162254.1835 631749.1396 376615.9535 83985.01421 977713.7296 2232318.02

319377.051 1230421.214 739400.9376 163886.4174 1901824.143 4354909.764

1568494.004 6038713.652 3597987.538 816574.1593 9400087.143 21421856.5

110380.8037 431169.2876 255883.1367 57483.25072 668631.4092 1523547.888

39524388.04

Normalized

0.2528

0.0565

0.1102

0.5420

0.0385

A˄32

Row sum

2.61738E+12 1.01094E+13 6.04071E+12 1.3543E+12 1.56769E+13 3.57987E+13

5.81986E+11 2.24798E+12 1.34323E+12 3.01139E+11 3.48597E+12 7.96031E+12

1.13809E+12 4.39583E+12 2.62668E+12 5.88869E+11 6.81666E+12 1.55661E+13

5.60297E+12 2.16415E+13 1.29313E+13 2.89922E+12 3.35603E+13 7.66353E+13

3.96977E+11 1.53338E+12 9.16222E+11 2.05412E+11 2.37785E+12 5.42984E+12

1.4139E+14

Normalized

0.2532

0.0563

0.1101

0.5420

0.0384

C. Linear Programming Method

Let A = [aij] be the pairwise comparison matrix. We can obtain the weights of the criteria or

alternatives by converting the comparison matrix into an Linear Programming problem. The

objective function of the LP problem then becomes –

Objective Function: ∑ ∑ 𝑍ij𝑛𝑗=𝑖+1

𝑛−1𝑖=1

Constraints:

Xi – Xj – Yij = ln aij (i)

Zij – Yij >= 0 (ii)

Zij – Yji >= 0 for i ≠ j (iii)

Xi – Xj >= 0 i, j = 1,2,3 … n ∀ aij > 1 (iv)

Xi – Xj >= 0 i, j = 1,2,3 … . n for all k ∀ aik ≥ ajk (v)

X1 = 0 (vi)

After obtaining the values of the decision variables the weights of the criteria or alternatives can be

found out. The weights are the antilog of Xi.

5. Pairwise comparison of songs for Location (L) by using Linear

programming

Location

ohz cgs Mtm ujj

Ohz 1.00 0.20 4.00 0.50

Cgs 5.00 1.00 7.00 5.00

Mtm 0.25 0.14 1.00 0.33

Ujj 2.00 0.20 3.00 1.00

Sum = 8.25 1.54 15.00 6.83

Normalised

Singer Ohz Cgs mtm ujj Average

(w)

ohz 0.12 0.13 0.27 0.07 0.15

cgs 0.61 0.65 0.47 0.73 0.61

mtm 0.03 0.09 0.07 0.05 0.06

ujj 0.24 0.13 0.20 0.15 0.18

0.598441 Ci = 0.095105

2.666589 Ri = 0.99

S x w =

0.243962

0.776325 Ci/Ri= 0.096066

Nmax =

4.285316

6. Pairwise comparison of songs for Actor (A) by using linear

programming method

actor

ohz cgs mtm ujj

ohz 1.00 3.00 0.25 0.20

cgs 0.33 1.00 0.14 0.17

mtm 4.00 7.00 1.00 2.00

ujj 5.00 6.00 0.50 1.00

Sum = 10.33 17.00 1.89 3.37

Singer Ohz cgs mtm ujj

Average (w)

Ohz 0.10 0.18 0.13 0.06 0.12

cgs 0.03 0.06 0.08 0.05 0.05

mtm 0.39 0.41 0.53 0.59 0.48

Ujj 0.48 0.35 0.26 0.30 0.35

0.468201 Ci = 0.068195

0.219607 Ri = 0.99

2.02213

1.494646 Ci/Ri= 0.068884

4.204584

RESULTS

Given below are the results for the criteria and the songs based on each criterion –

1. Weights for criteria

2 Weights for Lyrics

3 Weights for Music

4 Weights for Singer

Weight

0.405625

0.146843

0.360729

0.058322

0.028482

Weight

0.412965

0.142688

0.363452

0.049112

0.031782

Weight

0.2590

0.1904

0.3094

0.2194

0.0219

Weight

0.2532

0.0563

0.1101

0.5420

0.0384

5 Weights for Location

6 Weights for Actor

Final Result (Ranking)

lyrics music singer Location actor

O hsina julfho 0.427524 0.2590 0.2532 0.14 0.08

Akhiyo ke jharokhe 0.135754 0.1904 0.0563 0.69 0.08

sar jo tera 0.354691 0.3094 0.1101 0.03 0.42

ude jab jab 0.052575 0.2194 0.5420 0.14 0.42

Criteria Ranking

0.427524 0.317446 1

0.135754 0.142563 4

0.354691 0.24677 3

0.052575 0.264031 2

0.029456

Weight

0.14

0.69

0.03

0.14

Weight

0.08

0.08

0.42

0.42

FABRICS AND FALL FASHION

PART - 1

Our main objective function is to maximize profits. For this we have to find the optimal

number of units which we can sell for each product.

Given the price of Raw material and Labour and Machinery cost we can find the profit per

unit sold for each item as selling price of items are given. This calculation is done above.

In the Given question we have three type of constraints, one is upper limit of material to be

used, second is the maximum production according to the demand and third is minimum no.

of production.

Hence keeping in mind we have formed our Objective Function and constraints below.

Particulars

Price

Per Yard

($)

Tailored

Wool

Slacks

(x1)

Cashmer

e

Sweater

(x2)

Silk

Blouse

(x3)

Silk

Camisol

e

(x4)

Tailored

Skirt

(x5)

Wool

Blazer

(x6)

Velvet

Pants

(x7)

Cotton

Sweater

(x8)

Cotton

Miniskir

t

(x9)

Velvet

Shirt

(x10)

Button-

Down

Blouse

(x11)

Wool (in yards) 9.00 3.00 2.50

Acetate (in yards) 1.50 2.00 1.50 1.50 2.00

Cashmere (in yards) 60.00 1.50

Silk (in yards) 13.00 1.50 0.50

Rayon (in yards) 2.25 2.00 1.50

Velvet (in yards) 12.00 3.00 1.50

Cotton (in yards) 2.50 1.50 0.50

30.00 90.00 19.50 6.50 6.75 24.75 39.00 3.75 1.25 18.00 3.38

160.00 150.00 100.00 60.00 120.00 140.00 175.00 60.00 40.00 160.00 90.00

300.00 450.00 180.00 120.00 270.00 320.00 350.00 130.00 75.00 200.00 120.00

110.00 210.00 60.50 53.50 143.25 155.25 136.00 66.25 33.75 22.00 26.63

Material Cost (C1)

Labor and Machine Cost (C2)

Price (P)

Profit Per Unit Sold (Profit = P - C1 - C2) ($)

Constraints

<= 45000

<= 28000

<= 9000

<= 18000

<= 30000

<= 20000

<= 30000

<= 7000

<= 4000

<= 12000

<= 15000

<= 5500

<= 5000

<= 6000

<= 0

<= 0

>= 4200

>= 3000

>= 2800

x1 >= 0

x2 >= 0

x3 >= 0

x4 >= 0

x5 >= 0

x6 >= 0

x7 >= 0

x8 >= 0

x9 >= 0

x10 >= 0

x11 >= 0

Non Negativity : x9

Non Negativity : x10

Non Negativity : x11

Non Negativity : x3

Non Negativity : x4

Non Negativity : x5

Non Negativity : x6

Non Negativity : x7

Non Negativity : x8

Min. Production - Wool Blazer x6

Min. Production - Tailored Skirt x5

Non Negativity : x1

Non Negativity : x2

Min. Production - Silk Camisole x3 - x4

Min. Production - Cotton Miniskirt x8 - x9

Min. Production - Tailored Wool Slacks x1

Max. Production - Velvet Pants x7

Max. Production - Wool Blazer x6

Max. Production - Velvet Shirt x10

Max. Production - Cashmere Sweater x2

Max. Production - Silk Blouse x3

Max. Production - Silk Camisole x4

Velvet - Material Conatraint 3 x7 + 1.5 x10

Cotton - Material Conatraint 1.5 x8 + 0.5 x9

Max. Production - Tailored Wool Slacks x1

Cashmere - Material Conatraint 1.5 x2

Silk - Material Conatraint 1.5 x3 + 0.5 x4

Rayon - Material Conatraint 2 x5 + 1.5 x11

Objective Funtion : Maximize Profit : 110 x1 + 210 x2 + 60.5 x3 + 53.5 x4 + 143.25 x5 + 155.25 x6 + 136 x7 + 66.25 x8 + 33.75 x9 + 22 x10 + 26.63 x11

Wool - Material Conatraint 3 x1 + 2.5 x6

Acetate - Material Conatraint 2 x1 + 1.5 x6 + 2 x7

Solving the Equations and Finding the Maximum Profit by Using

EXCEL SOLVER.

Tailored

Wool

Slacks

(x1)

Cashmer

e

Sweater

(x2)

Silk

Blouse

(x3)

Silk

Camisole

(x4)

Tailored

Skirt

(x5)

Wool

Blazer

(x6)

Velvet

Pants

(x7)

Cotton

Sweater

(x8)

Cotton

Miniskirt

(x9)

Velvet

Shirt

(x10)

Button-

Down

Blouse

(x11)

4200 4000 7000 15000 8066.67 5000 0 0 60000 6000 9244.44

110.00 210.00 60.50 53.50 143.25 155.25 136.00 66.25 33.75 22.00 26.63

Constraints LHS Sign RHS

3.00 2.50 0 <= 45000

2.00 1.50 1.50 2.00 0 <= 28000

1.50 0 <= 9000

1.50 0.50 0 <= 18000

2.00 1.50 0 <= 30000

3.00 1.50 0 <= 20000

1.50 0.50 0 <= 30000

1.00 0 <= 7000

1.00 0 <= 4000

1.00 0 <= 12000

1.00 0 <= 15000

1.00 0 <= 5500

1.00 0 <= 5000

1.00 0 <= 6000

1.00 -1.00 0 <= 0

1.00 -1.00 0 <= 0

1.00 0 >= 4200

1.00 0 >= 3000

1.00 0 >= 2800

1.00 0 >= 0

1.00 0 >= 0

1.00 0 >= 0

1.00 0 >= 0

1.00 0 >= 0

1.00 0 >= 0

1.00 0 >= 0

1.00 0 >= 0

1.00 0 >= 0

1.00 0 >= 0

1.00 0 >= 0

Non Negativity : x7

Non Negativity : x8

Non Negativity : x9

Non Negativity : x10

Non Negativity : x11

Non Negativity : x1

Non Negativity : x2

Non Negativity : x3

Non Negativity : x4

Non Negativity : x5

Non Negativity : x6

Max. Production - Velvet Shirt

Min. Production - Silk Camisole

Min. Production - Cotton Miniskirt

Min. Production - Tailored Wool

Min. Production - Wool Blazer

Min. Production - Tailored Skirt

Max. Production - Tailored Wool

Max. Production - Cashmere Sweater

Max. Production - Silk Blouse

Max. Production - Silk Camisole

Max. Production - Velvet Pants

Max. Production - Wool Blazer

Acetate - Material Conatraint

Cashmere - Material Conatraint

Silk - Material Conatraint

Rayon - Material Conatraint

Velvet - Material Conatraint

Cotton - Material Conatraint

Particulars Max Profit ($)

No. of Units to be Produced6862933.33

Objective Funtion : Maximize Profit

Wool - Material Conatraint

PART - 2

Now if the Constraint is given that the Velvet material could not be returned back then whole of velvet

material available should be used.

We can see in the above solution that the Velvet shirts are produced to the maximum limit but velvet

shirts are not being produced in order to maximize the profit.

Hence in the above constraints we shall change only one constraint: Velvet Material Constraints:

3x7+1.5x10=20000

In above constraint we have removed the less than (<) condition as we now have to use the whole

material.

Solving the Equations and Finding the Maximum Profit by Using

EXCEL SOLVER.

As by fully utilizing the Velvet She is gaining lesser profit hence she should not change her change her

decision and stick to the first plan of production. The balance material she can keep with herself.

Tailored

Wool

Slacks

(x1)

Cashmer

e

Sweater

(x2)

Silk

Blouse

(x3)

Silk

Camisole

(x4)

Tailored

Skirt

(x5)

Wool

Blazer

(x6)

Velvet

Pants

(x7)

Cotton

Sweater

(x8)

Cotton

Miniskirt

(x9)

Velvet

Shirt

(x10)

Button-

Down

Blouse

(x11)

4200 4000 7000 15000 3177.78 5000 3666.67 0 60000 6000 15763

110.00 210.00 60.50 53.50 143.25 155.25 136.00 66.25 33.75 22.00 26.63

Constraints LHS Sign RHS

3.00 2.50 0 <= 45000

2.00 1.50 1.50 2.00 0 <= 28000

1.50 0 <= 9000

1.50 0.50 0 <= 18000

2.00 1.50 0 <= 30000

3.00 1.50 0 = 20000

1.50 0.50 0 <= 30000

1.00 0 <= 7000

1.00 0 <= 4000

1.00 0 <= 12000

1.00 0 <= 15000

1.00 0 <= 5500

1.00 0 <= 5000

1.00 0 <= 6000

1.00 -1.00 0 <= 0

1.00 -1.00 0 <= 0

1.00 0 >= 4200

1.00 0 >= 3000

1.00 0 >= 2800

1.00 0 >= 0

1.00 0 >= 0

1.00 0 >= 0

1.00 0 >= 0

1.00 0 >= 0

1.00 0 >= 0

1.00 0 >= 0

1.00 0 >= 0

1.00 0 >= 0

1.00 0 >= 0

1.00 0 >= 0

Non Negativity : x7

Non Negativity : x8

Non Negativity : x9

Non Negativity : x10

Non Negativity : x11

Non Negativity : x1

Non Negativity : x2

Non Negativity : x3

Non Negativity : x4

Non Negativity : x5

Non Negativity : x6

Max. Production - Velvet Shirt

Min. Production - Silk Camisole

Min. Production - Cotton

Min. Production - Tailored Wool

Min. Production - Wool Blazer

Min. Production - Tailored Skirt

Max. Production - Tailored Wool

Max. Production - Cashmere

Max. Production - Silk Blouse

Max. Production - Silk Camisole

Max. Production - Velvet Pants

Max. Production - Wool Blazer

Acetate - Material Conatraint

Cashmere - Material Conatraint

Silk - Material Conatraint

Rayon - Material Conatraint

Velvet - Material Conatraint

Cotton - Material Conatraint

Particulars Max Profit ($)

No. of Units to be Produced6834822.22

Objective Funtion : Maximize Profit

Wool - Material Conatraint