CMA Final · Strategic Cost Management · Linear Programming
Bharat Tools maximises Z = 4x + 2y subject to 2x + y ≤ 10, x ≤ 4, y ≤ 8 and x, y ≥ 0. Which statement is correct?
The problem has multiple optimal solutions, each giving Z = 20. The objective function 4x + 2y is twice the left side of the binding constraint 2x + y ≤ 10, so the objective line is parallel to that edge. The whole segment from (4,2) to (1,8) is optimal.
- AThe unique optimum is x=4, y=2 with Z=20
- BThe problem is unbounded
- CThe unique optimum is x=1, y=8 with Z=20
- DThere are multiple optimal solutions, all giving Z=20Correct
Explanation
The corner points are (0,0) with Z=0, (4,0) with 16, (4,2) with 20, (1,8) with 20 and (0,8) with 16. The objective line is parallel to the constraint 2x+y=10, because 4x+2y = 2(2x+y). So every point on the segment from (4,2) to (1,8) gives Z=20. Calling either end point the unique optimum ignores this alternative-optima situation.
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