CMA Final · Strategic Cost Management · Linear Programming
A hostel mess in Pune wants to minimise the cost Z = 3x + 4y (Rs) of a mix of two foods. The nutrient constraints are x + y ≥ 10 and x + 3y ≥ 18, with x, y ≥ 0. What is the minimum cost?
The minimum cost is Rs 34, reached at x = 6 and y = 4, where the two nutrient constraints intersect. The other corner points (0, 10) and (18, 0) cost Rs 40 and Rs 54, both higher.
- ARs 34Correct
- BRs 40
- CRs 54
- DRs 72
Explanation
The corner points of the unbounded region are (0,10), (6,4) and (18,0). (6,4) is where x + y = 10 meets x + 3y = 18. The costs are: (0,10) gives 40, (6,4) gives 18 + 16 = 34, and (18,0) gives 54. The minimum is 34. Rs 72 would come from swapping the cost coefficients at (18,0), and 72 is not a corner cost anyway.
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