The document discusses the Analytical Hierarchy Process (AHP), a structured decision-making technique that quantifies complex choices by organizing them into a hierarchy of criteria and alternatives. It includes methodologies such as pairwise comparisons and various mathematical approaches, like eigenvalue and linear programming methods, to evaluate options based on defined criteria. AHP is particularly useful in complex decision-making scenarios, such as selecting the best song from a set of alternatives based on multiple criteria.

1. ADVANCED MANAGEMENT
SCIENCE
PROJECT ON ANALYTICAL
HEIRARCHY PROCESS AND
FABRICS AND FALL FASHION
Submitted to:
DR. G.N. Patel
Submitted by:
UDIT JAIN
13DM206

2. 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.

3. 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

4. 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

5.  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

6. 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.

7. 1. Pairwise comparisonofcriteria (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 comparisonof songs for Lyrics (Lr) by Eigenvalue 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

8. 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 comparisonofsongs 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

9. A˄2
Rowsum
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
Rowsum
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

10. Normalised
0.2593
0.1904
0.3111
0.2172
0.0220
A˄32
Rowsum
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 comparisonofsongs 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
Rowsum
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

11. Normalized
0.2817
0.0420
0.0999
0.5482
0.0282
A˄4
Rowsum
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
Rowsum
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

12. A˄32
Rowsum
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: ∑ ∑ 𝑍ij𝑛
𝑗=𝑖+1
𝑛−1
𝑖=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.

13. 5. Pairwise comparisonofsongs 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

15. 6. Pairwise comparisonofsongs 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

17. 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

18. 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

19. 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
($)
Tailored
Wool
Slacks
(x1)
Cashmer
e
Sweater
(x2)
Silk
Blouse
(x3)
Silk
Camisol
e
(x4)
Tailored
Skirt
(x5)
Wool
Blazer
(x6)
Velvet
Pants
(x7)
Cotton
Sweater
(x8)
Cotton
Miniskir
t
(x9)
Velvet
Shirt
(x10)
Button-
Down
Blouse
(x11)
Wool (in yards) 9.00 3.00 2.50
Acetate (in yards) 1.50 2.00 1.50 1.50 2.00
Cashmere (in yards) 60.00 1.50
Silk (in yards) 13.00 1.50 0.50
Rayon (in yards) 2.25 2.00 1.50
Velvet (in yards) 12.00 3.00 1.50
Cotton (in yards) 2.50 1.50 0.50
30.00 90.00 19.50 6.50 6.75 24.75 39.00 3.75 1.25 18.00 3.38
160.00 150.00 100.00 60.00 120.00 140.00 175.00 60.00 40.00 160.00 90.00
300.00 450.00 180.00 120.00 270.00 320.00 350.00 130.00 75.00 200.00 120.00
110.00 210.00 60.50 53.50 143.25 155.25 136.00 66.25 33.75 22.00 26.63
Material Cost (C1)
Labor andMachine Cost (C2)
Price (P)
Profit Per Unit Sold(Profit = P - C1 - C2)($)

20. 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 -SilkCamisole x3 - x4
Min.Production -Cotton Miniskirt x8 - x9
Min.Production -Tailored Wool Slacks x1
Max.Production -VelvetPants x7
Max.Production -Wool Blazer x6
Max.Production -VelvetShirt x10
Max.Production -CashmereSweater x2
Max.Production -SilkBlouse x3
Max.Production -SilkCamisole x4
Velvet-Material Conatraint 3x7 + 1.5x10
Cotton -Material Conatraint 1.5x8 + 0.5x9
Max.Production -Tailored Wool Slacks x1
Cashmere-Material Conatraint 1.5x2
Silk-Material Conatraint 1.5x3 + 0.5x4
Rayon -Material Conatraint 2x5 + 1.5x11
ObjectiveFuntion: MaximizeProfit: 110x1 + 210x2 + 60.5x3 + 53.5x4 + 143.25x5 + 155.25x6 + 136x7 + 66.25x8 + 33.75x9 + 22x10 + 26.63x11
Wool -Material Conatraint 3x1 + 2.5x6
Acetate-Material Conatraint 2x1 + 1.5x6 +2x7

21. 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 -SilkCamisole
Min.Production -Cotton Miniskirt
Min.Production -Tailored Wool
Min.Production -Wool Blazer
Min.Production -Tailored Skirt
Max.Production -Tailored Wool
Max.Production -CashmereSweater
Max.Production -SilkBlouse
Max.Production -SilkCamisole
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 MaxProfit($)
No.ofUnitsto beProduced
6862933.33
ObjectiveFuntion : MaximizeProfit
Wool -Material Conatraint

22. 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.

23. 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.ofUnits to be Produced
6834822.22
Objective Funtion : Maximize Profit
Wool - Material Conatraint