CMA Final · Strategic Cost Management · Assignment
A firm has three salespersons P, Q and R and three territories T1, T2 and T3. Expected monthly profit (₹ thousand) is: P: 40, 35, 30; Q: 38, 42, 36; R: 33, 31, 39 (for T1, T2, T3 respectively). Each salesperson takes exactly one territory. What is the maximum total profit?
The maximum profit is ₹121 thousand. Assign P to T1 earning 40, Q to T2 earning 42 and R to T3 earning 39. The other five possible assignments give between 99 and 112 thousand, so this one is the best under the maximisation form of the assignment problem.
- A₹107 thousand
- B₹112 thousand
- C₹121 thousandCorrect
- D₹105 thousand
Explanation
For maximisation, subtract every entry from the largest value (42) to form a regret matrix and then minimise. Equivalent enumeration of the six assignments gives profits of 121, 107, 112, 104, 99 and 105. The best is P-T1 (40) + Q-T2 (42) + R-T3 (39) = 121. Choosing 112 would result from P-T2, Q-T1, R-T3, which is not optimal.
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