For a linear programming problem with a non-empty bounded feasible region, where does an optimal solution occur if one exists?
Correct answer: D. At an extreme point of the feasible region
- A. At a point outside the feasible region
- B. At the midpoint of every feasible line segment
- C. At the point nearest to the coordinate origin
- D. At an extreme point of the feasible region
Explanation
The fundamental theorem of linear programming states that an optimum occurs at an extreme point when the feasible region is non-empty and bounded. If several points give the same optimum, an entire edge may also be optimal.
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About Linear Programming
Linear programming models the maximum or minimum of an objective function subject to linear constraints. Questions involve translating word conditions into inequalities, drawing the feasible region, identifying corner points and evaluating the objective function, including cases involving non-negativity restrictions and redundant constraints.
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