CMA Intermediate · Operations Management and Strategic Management · Optimum Allocation of Resources - LPP
A firm maximises Z = 5x + 4y subject to x + y <= 10, x <= 6, and x, y >= 0. What is the optimal value of Z?
The optimal value is 46, reached at x = 6 and y = 4. Evaluating Z at the corner points (0,0), (6,0), (0,10) and (6,4) gives 0, 30, 40 and 46, so the highest value is 46. Using x = 10 would break the x <= 6 limit.
- A46Correct
- B50
- C40
- D44
Explanation
Corner points: (0,0)=0, (6,0)=30, (0,10)=40, (6,4)=30+16=46. The maximum is 46 at (6,4). Option 50 assumes x=10, which violates x<=6; option 40 ignores the intersection point.
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