CMA Intermediate · Operations Management and Strategic Management · Optimum Allocation of Resources - LPP
A company must produce at least 60 units in total of products A and B (x + y >= 60), and at most 40 units of A (x <= 40). Cost is minimised: Z = 8x + 12y, x,y >= 0. Further, y <= 50. What is the minimum cost in rupees?
The minimum cost is Rs 560, at x = 40 and y = 20. Product A is cheaper, so it is used up to its limit of 40 units, and B makes up the remaining 20 units to meet the 60-unit requirement: 8×40 + 12×20 = 560.
- ARs 480Correct
- BRs 720
- CRs 600
- DRs 560
Explanation
Cost is lower for A, so use as much A as is allowed? Check corners of feasible region: (40,20)=320+240=560; (40,50)=320+600=920; (10,50)=80+600=680; (60,0) is infeasible as x<=40. Taking x+y=60 with x=40,y=20 gives 560, which is the minimum among the corners. So the minimum is Rs 560, not 480.
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