# Find the Max and Mini values of the objective function Z=3x+4y on the region bounded by 2x+y>5x+5y>162x+y<14 -x+4y<20Needs to be solved with the simplex method

Question

Find the Max and Mini values of the objective function Z=3x+4y on the region bounded by

2x+y>5

x+5y>16

2x+y<14

-x+4y<20

Needs to be solved with the simplex method

Step 1

First find the minimum value: so, the problem is,

Min Z = 3 x1 + 4 x2

Subject to

2x1 + x2 > 5

x1 + 5x2 > 16

2x1 + x2 < 14

-x1 + 4x2 < 20

And x1, x2 0

Now, Max Z = -3 x1 – 4 x2

The problem is converted to canonical form by adding slack, surplus and artificial variable:

Max Z = -3 x1 - 4 x2 + 0 S1 + 0 S2 + 0 S3 +0 S4 -MA1-MA2

Subject to

2x1 + x2 - S1                     + A1            = 5

x1 + 5x2        - S2                      + A2 =16

2x1 + x2                      + S3                                    =14

-x1 + 4x2                      + S4                       =20

And x1, x2, S1, S2, S3, S4, A1, A2 0

Iteration 1

.

Step 2

Pivot element is 5 and leaving basis variable is A2 and entering variable is x2.

Iteration table 2:

Step 3

Pivot element is 1.8, entering = x1 and leaving basis is A1

Iteration ...

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