CMA Final · Strategic Cost Management · Linear Programming

Ganga Plastics maximises profit Z = cA·A + 50B, where machine hours 3A + 2B ≤ 120 and labour hours A + 2B ≤ 80, with A, B ≥ 0. With cA = 40, the optimum is A=20, B=30. Over what range of cA (₹ per unit of A) does this product mix remain optimal, with the profit on B fixed at ₹50?

The mix A = 20, B = 30 stays optimal for cA between ₹25 and ₹75. The objective-function slope must lie between the slopes of the two binding constraints, -3/2 and -1/2. At the end values, profit ties with an adjacent corner point.

A₹20 to ₹60
B₹25 to ₹75Correct
C₹30 to ₹80
D₹40 to ₹75

Explanation

The optimum at (20,30) lies where 3A+2B=120 (slope -3/2) and A+2B=80 (slope -1/2) meet. It stays optimal while the objective slope -cA/50 lies between -3/2 and -1/2, so cA lies between 25 and 75. Check: at cA=75, Z at (20,30) and at (40,0) both equal 3,000. At cA=25, Z at (20,30) and at (0,40) both equal 2,000. Using only the current value of 40 as a bound is the error in the last option.

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Ganga Plastics maximises profit Z = cA·A + 50B, where machine hours 3A + 2B ≤ 120 and labour hours A + 2B ≤ 80, with A, B ≥ 0. With cA = 40, the optimum is A=20, B=30. Over what range of cA (₹ per unit of A) does this product mix remain optimal, with the profit on B fixed at ₹50?

Explanation

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