Question

SIMPLEX METHOD Solve the following problem using simplex method LP MODEL Let X1 no. of batches of Bluebottles X2 no. of batches of Cleansweeps Objective: Max Z-10X1+20X2 Subject to: 3X1 4X2 S 3 Plant 1 assembly capacity constraint -X1 2-5 5X1 +6X2 s 18 Z, X1, X2 20 Plant 2 capacity constraint Plant 3 capacity constraint

Answer 1

Standard form

Max Z = 10x1 + 20x2 + 0s1 + 0s2 + 0s3
s.t.
3x1 + 4x2 + 1s1 + 0s2 + 0s3 = 31
1x1 + 0x2 + 0s1 + 1s2 + 0s3 = 5
-5x1 + 6x2 + 0s1 + 0s2 + 1s3 = 18
x1, x2, s1, s2, s3 >= 0

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Note that at the end of the second iteration, all the Cj - Zj values are <= 0. So, we have reached optimality. The optimal solution is:

x1 = 3
x2 = 5.5
Max Z = 140