CMA Intermediate · Operations Management and Strategic Management · Optimum Allocation of Resources - LPP
A firm maximises profit subject to the constraints x + y <= 4 and x + y >= 9, with x, y >= 0. What does the graphical method show?
The problem is infeasible. One constraint requires x+y to be no more than 4 while the other requires it to be at least 9, so no point can satisfy both. With no common feasible region, no optimal solution exists whatever the objective function is.
- AUnbounded solution with infinite profit
- BUnique optimum at the origin
- CMultiple optimal solutions along x + y = 4
- DInfeasible problem with no common feasible regionCorrect
Explanation
The first constraint requires x+y to be at most 4, while the second needs it to be at least 9. No point can satisfy both, so the feasible region is empty. Hence the LPP is infeasible. The origin fails the second constraint since 0 is less than 9.
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