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CMA Intermediate · Operations Management and Strategic Management · Job Evaluation, Job Allocation - Assignment

In a maximisation assignment problem, the largest profit is ₹30 thousand. The opportunity-loss matrix (30 minus each profit) is solved for three assignments and the minimum total loss is ₹14 thousand. What is the maximum total profit of the original problem?

The maximum profit is ₹76 thousand. With three assignments, the total of maximum entries is 3 × 30 = 90, and the minimum total opportunity loss of 14 is subtracted from it. Equivalently, summing the original profits of the chosen cells gives 76.

  1. A₹76 thousandCorrect
  2. B₹90 thousand
  3. C₹104 thousand
  4. D₹14 thousand

Explanation

Each assigned cell has loss = 30 - profit. For three assignments, total loss = 3×30 - total profit. So profit = 90 - 14 = 76 thousand. Reporting 90 ignores the loss, and adding 14 gives 104, which is the wrong sign.

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