CMA Final · Strategic Cost Management · Linear Programming
Maximise Z = c·x + 4y subject to 6x + 4y ≤ 24, x + 2y ≤ 6, x, y ≥ 0. With c = 5 the optimum is x = 3, y = 1.5. Within what range of the profit per unit c of x does this product mix stay optimal?
The mix stays optimal for c between ₹2 and ₹6. At the corner (3,1.5), Z = 3c + 6, which must be at least 4c from corner (4,0), giving c ≤ 6, and at least 12 from corner (0,3), giving c ≥ 2.
- A₹2 to ₹6Correct
- B₹4 to ₹6
- C₹2 to ₹8
- D₹1 to ₹3
Explanation
The corners are (4,0), (3,1.5) and (0,3), with Z = 4c, 3c+6 and 12. (3,1.5) beats (4,0) when 3c+6 ≥ 4c, so c ≤ 6. It beats (0,3) when 3c+6 ≥ 12, so c ≥ 2. The range is therefore 2 ≤ c ≤ 6. Equivalently, the ratio c/4 must lie between the constraint slopes 1/2 and 3/2.
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