CMA Intermediate · Operations Management and Strategic Management · Job Evaluation, Job Allocation - Assignment
A firm wants to maximise profit by assigning Workers A, B and C to Jobs 1, 2 and 3 (one each). Profits in ₹ thousand are: A: 14, 10, 12; B: 11, 13, 9; C: 10, 8, 12 (Jobs 1, 2, 3). Worker C is not permitted to do Job 3. What is the maximum total profit (₹ thousand)?
The maximum profit is ₹35 thousand. The unrestricted best of 39 needs Worker C on Job 3, which is prohibited. Among the remaining assignments, Worker A on Job 3, B on Job 2 and C on Job 1 gives 12+13+10 = 35, the highest feasible total.
- A33
- B35Correct
- C39
- D31
Explanation
Without the restriction the best is A-1, B-2, C-3 = 14+13+12 = 39. That uses C-3 and so is not allowed, as is A-2, B-1, C-3 (33). The feasible totals are 31, 29, 31 and 35, with A-3, B-2, C-1 giving 14... precisely 12+13+10 = 35. So the maximum is 35.
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