CMA Final · Strategic Cost Management · Assignment
A works manager at a Pune plant must allocate 5 supervisors to 5 production lines, one supervisor per line, and wants to test every possible complete allocation by brute force before using the Hungarian method. How many distinct complete assignments exist?
There are 120 distinct complete assignments, because a one-to-one allocation of 5 supervisors to 5 lines is a permutation, 5 factorial. Choices shrink from 5 to 4 to 3 to 2 to 1 as each line is filled, so 5^5 would wrongly allow repeated use of a line.
- A25
- B60
- C120Correct
- D3125
Explanation
The first supervisor can go to any of 5 lines, the next to 4, and so on, giving 5! = 5×4×3×2×1 = 120 complete assignments. 3125 (5^5) wrongly lets one line take several supervisors, and 25 counts only the cells of the matrix.
Did you get it right without looking?
One question tells you little. A timed set on Assignment shows your real accuracy, how long you take and where you lose marks.
More Assignment questions
- Three technicians A, B and C are to be assigned one each to three jobs J1, J2 and J3. The cost (₹ '000) is: A: 9, 11, 14; B: 12, 7, 10; C: 8…
- Three workers W1, W2, W3 are available for four jobs J1 to J4, and each worker can take at most one job; one job stays unassigned. Costs (Rs…
- 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…
- A works manager has 5 operators and only 4 jobs, each operator can do any job, and the cost of every operator-job pair is known. Before appl…
- 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,…
- Arjun Fabricators must assign three jobs (A, B, C) to three machines (M1, M2, M3), one job per machine. Processing costs in Rs thousand are:…