sensitivity analysis-case ii

8/11/2019 Sensitivity Analysis-Case II

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Case 2

Knitting Department

Submitted to- Dr. Hitesh Arora

By-

Abhijeet Agarwal 231005

Abhinav Joshi 231007

Atin Garg 231036


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X1= Units of Product 1

X2 = Units of Product 2

X3 = Units of Product 3

Maximize Z= 7x1 + 3x2 + 9x3 (Profit)

S.t.

Labour 4x1 + 5x2 + 6x3


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7 3 9 0 0 0

B.V Cb X1 X2 X3 S1 S2 S3 Sol. Ratio

S1 0 4 5 6 1 0 0 360 60

S2 0 2 4 6 0 1 0 300 50

S3 0 9 5 6 0 0 1 600 100

Cj-Zj 7 3 9 0 0 0


S1 0 2 1 0 1 -1 0 60 30

X3 9 1/3 2/3 1 0 1/6 0 50 150

S3 0 7 1 0 0 -1 1 300 300/7

Cj-Zj 4 -3 0 0 -3/2 0


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7 3 9 0 0 0


X1 7 1 0 -1/2 0 30 -

X3 9 0 1 -1/6 1/3 0 40 120

S3 0 0 -5/2 0 -7/2 5/2 1 90 36

Cj-Zj 0 -5 0 -2 0

B.V Cb X1 X2 X3 S1 S2 S3 Sol.

X1 7 1 0 0 -1/5 0 1/5 48

X3 9 0 5/6 1 3/10 0 -2/15 28

S2 0 0 -1 0 -7/5 -1 2/5 36

Cj-Zj 0 -9/2 0 -13/10 0 -1/5


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Maximize Z 588

Units of Product I 48

Units of Product II 0

Units of Product III 28

Labor Usage 360


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Adjustable Cells

Final Reduced Objective Allowable Allowable

Cell Name Value Cost Coefficient Increase Decrease

$E$4 x1 48 0 7 6.5 1

$E$5 x2 0 -4.5 3 4.5 1E+30

$E$6 x3 28 0 9 1.5 4.333333333

Constraints

Final Shadow Constraint Allowable Allowable

Cell Name Value Price R.H. Side Increase Decrease

$D$8 Labor Usage x3 360 1.3 360 25.71428571 93.33333333

$D$9

Machine Usage

x3 264 0 300 1E+30 36

$D$10

Material Usage

x3 600 0.2 600 210 90


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As P1 is a basic variable,so for basic variable

Maxykj>0{Cj-Zj /ykj}


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As allowable increase is 6.5 so increasing by 3would not impact the optimal solution

But as coefficient of x1 will change

Hence new Z=732

Which is shown by excel solver.

Q4-What would the values in the optimal solution be if

the objective coefficient of x1 were to increased by 3?


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For labour constraint

Maxbik>0{-Xbi / bik}


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Q6- What would the values in the optimal solution be if

the amount of labor available decreased by 10 hours?

From the excel solver solution

Z= 575

x1=50x2=0

X3=25


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For material constraint

Max bik>0{-Xbi / bik}


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sensitivity analysis-case ii

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