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Maximize $Z = 15X_1 + 20X_2$ subject to $12X_1 + 4X_2 \ge 36$, $12X_1 - 6X_2 \le 24$, $X_1, X_2 \ge 0$. The above linear programming problem has

1. infeasible solution
2. unbounded solution
3. alternative optimum solutions
4. degenerate solution

Correct answer: alternative optimum solutions

Solution

The feasible region formed by the constraints allows the objective function to attain the same maximum value along an edge rather than at a single point. This indicates multiple optimal solutions. Hence, the problem has alternative optimum solutions.

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