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CMA Intermediate · Operations Management and Strategic Management · Optimum Allocation of Resources - LPP

Maximise Z = 40x1 + 30x2 subject to x1 + x2 ≤ 80, 2x1 + x2 ≤ 100, x1, x2 ≥ 0, using the simplex method. What is the optimal value of Z?

The optimal value of Z is ₹2,600. The simplex iterations move from the origin to x1 = 50, then to x1 = 20 and x2 = 60, where all Cj − Zj values are non-positive. Z = 40×20 + 30×60 = 2,600, higher than the other corner points.

  1. A₹2,600Correct
  2. B₹2,400
  3. C₹2,000
  4. D₹3,200

Explanation

Iteration 1: x1 enters (40 is largest); ratios 80/1 = 80 and 100/2 = 50, so s2 leaves and x1 = 50. Then x2 has Cj − Zj = 30 − 20 = 10 > 0 and enters; ratios 30/0.5 = 60 and 50/0.5 = 100, so s1 leaves. This gives x2 = 60 and x1 = 20, so Z = 800 + 1,800 = 2,600. The value 2,400 is only the vertex (0, 80) and 2,000 is the vertex (50, 0). The value 3,200 ignores the second constraint.

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