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CMA Final · Strategic Cost Management · Assignment

Three operators W1, W2 and W3 are available for four jobs J1 to J4; each operator can do only one job and one job will remain undone. Costs (₹ thousand) for J1, J2, J3, J4 are: W1: 10, 14, 12, 16; W2: 13, 11, 15, 14; W3: 12, 15, 11, 13. The unbalanced problem is balanced by adding a dummy operator with zero cost. What is the minimum total cost and which job is left unassigned?

The minimum cost is ₹32 thousand with J4 left unassigned. After adding a zero-cost dummy operator, the best allocation is W1 to J1 at 10, W2 to J2 at 11 and W3 to J3 at 11. Leaving out any other job costs at least 34 thousand.

  1. A₹32 thousand; J4 unassignedCorrect
  2. B₹34 thousand; J3 unassigned
  3. C₹35 thousand; J2 unassigned
  4. D₹36 thousand; J1 unassigned

Explanation

Adding a dummy row of zeros, the job given to the dummy is the one left undone. Best totals by omitted job are: J1 omitted 36 (W1-J3, W2-J2, W3-J4); J2 omitted 35 (W1-J1, W2-J4, W3-J3); J3 omitted 34 (W1-J1, W2-J2, W3-J4); J4 omitted 32 (W1-J1, W2-J2, W3-J3). The minimum is 32 with J4 unassigned.

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