CMA Final · Strategic Cost Management · Assignment
Three workers W1, W2, W3 are available for four jobs J1 to J4, and each worker can take at most one job; one job stays unassigned. Costs (Rs hundred) for J1, J2, J3, J4: W1: 12, 10, 15, 8; W2: 9, 14, 11, 13; W3: 16, 12, 10, 14. What is the minimum total cost?
The minimum cost is Rs 27 hundred. After adding a dummy worker, W1 takes J4 (8), W2 takes J1 (9) and W3 takes J3 (10), leaving J2 unassigned. Each worker gets the cheapest job in a distinct column, so no cheaper plan exists.
- ARs 29 hundred
- BRs 31 hundred
- CRs 27 hundredCorrect
- DRs 25 hundred
Explanation
Add a dummy worker with zero costs to balance the problem. The row minima are W1 = 8 (J4), W2 = 9 (J1), W3 = 10 (J3). They fall in different columns, so the total 8+9+10 = 27 is achievable and optimal, leaving J2 unassigned. Rs 29 arises from W1-J2, W2-J1, W3-J3, which is feasible but costlier.
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