Find the Max and Mini values of the objective function Z=3x+4y on the region bounded by
Needs to be solved with the simplex method
First find the minimum value: so, the problem is,
Min Z = 3 x1 + 4 x2
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
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
Pivot element is 5 and leaving basis variable is A2 and entering variable is x2.
Iteration table 2:
Pivot element is 1.8, entering = x1 and leaving basis is A1
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