CMA Intermediate · Operations Management and Strategic Management · Optimum Allocation of Resources - LPP
Maximise Z = 4x + 6y subject to 2x + 3y <= 12, x <= 5, x, y >= 0. Which statement is correct?
The problem has multiple optimal solutions with maximum Z of 24. The objective function is exactly twice the left side of the constraint 2x+3y<=12, so the iso-profit line coincides with that constraint edge. Every point on the edge from (0,4) to (5, 2/3) yields the same Z of 24.
- AUnique optimum at (5, 0) with Z = 20
- BUnique optimum at (0, 4) with Z = 24
- CMultiple optimal solutions; maximum Z = 24 attained along the segment from (0, 4) to (5, 2/3)Correct
- DNo feasible solution exists
Explanation
The objective 4x+6y is 2 times (2x+3y), so the iso-profit line is parallel to the constraint 2x+3y=12. Every point on that line within the region gives Z = 24. Corner points (0,4) and (5, 2/3) both give 24: 4*5+6*(2/3)=20+4=24. Choosing a single point such as (0,4) as unique ignores the parallel line.
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