CMA Final · Strategic Cost Management · Assignment
A firm assigns salesmen P, Q, R one each to territories X, Y, Z to maximise monthly profit (Rs thousand). Profits for X, Y, Z: P: 40, 35, 25; Q: 30, 20, 35; R: 45, 30, 20. What is the maximum total profit?
The maximum profit is Rs 115 thousand, achieved by sending P to Y, Q to Z and R to X (35+35+45). Giving P his best territory X lowers the total to Rs 105 thousand, so a greedy choice is not optimal.
- ARs 105 thousand
- BRs 115 thousandCorrect
- CRs 90 thousand
- DRs 85 thousand
Explanation
Evaluate all six assignments: PX-QY-RZ 80; PX-QZ-RY 105; PY-QX-RZ 85; PY-QZ-RX 115; PZ-QX-RY 85; PZ-QY-RX 90. The maximum is 115 (P-Y, Q-Z, R-X). The 105 option results from giving P its personal best territory X, which blocks R's 45.
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