In a linear programming problem, if the feasible region is bounded, where does the optimal (maximum or minimum) value of the objective function always occur?
Answer and explanation
Correct answer: D. At a corner point (vertex) of the feasible region
- Step 1: According to the Fundamental Theorem of Linear Programming (Corner Point Theorem), the objective function attains its optimal values at the boundary vertices.
- Step 2: For any bounded feasible polygonal region, maximum and minimum values occur at one or more corner points.
Answer
At a corner point (vertex) of the feasible region.
Why not the others: The origin may lie outside the feasible region; interior points never achieve optimal values in linear constraints; and optimality is not restricted to coordinate axes.
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