CMA Final · Strategic Cost Management · Linear Programming
A Nashik feed mill minimises cost C = 6x + 8y (₹ per unit) subject to 2x + y ≥ 12, x + 2y ≥ 12, x, y ≥ 0. What is the minimum cost?
The minimum cost is ₹56, reached at x = 4 and y = 4. The feasible region has corners (0,12), (4,4) and (12,0), costing ₹96, ₹56 and ₹72 respectively, and the lowest of these is the optimum for a minimisation problem.
- A₹56Correct
- B₹72
- C₹96
- D₹48
Explanation
The corner points of the feasible region are (0,12), (4,4) and (12,0). Costs are 6(0)+8(12)=96, 6(4)+8(4)=56 and 6(12)+8(0)=72. The minimum is 56 at (4,4). Taking 72 means looking only at an axis point and ignoring the intersection of the two constraints.
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