CMA Final · Strategic Cost Management · Linear Programming
Kaveri Tools Ltd maximises Z = 50x + 40y (Rs contribution) from products A and B. The constraints are machine hours 2x + y ≤ 100, labour hours x + y ≤ 70, and x, y ≥ 0. The optimum is at x = 30, y = 40. What is the shadow price (value of one extra hour) of machine hours?
The shadow price of machine hours is Rs 10 per hour. One extra machine hour moves the optimum from (30, 40) to (31, 39), raising contribution from Rs 3,100 to Rs 3,110. The Rs 30 figure belongs to labour hours.
- ARs 10Correct
- BRs 30
- CRs 40
- DRs 50
Explanation
Both constraints bind at the optimum, so Z = 1,500 + 1,600 = 3,100. With machine hours at 101 and labour at 70, x + y = 70 and 2x + y = 101 give x = 31, y = 39. Z = 1,550 + 1,560 = 3,110, so the gain is Rs 10. Rs 30 is the shadow price of labour hours (Z rises to 3,130 when labour is 71), which is the wrong resource.
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