If a primal maximization problem and its dual minimization problem are both feasible, which relationship must hold for any feasible pair of solutions?
Correct answer: B. The primal value cannot exceed the dual value
- A. The dual value must equal the primal value
- B. The primal value cannot exceed the dual value
- C. The primal value must exceed the dual value
- D. The two objective values must both be zero
Explanation
Weak duality states that every feasible primal maximization value is less than or equal to every feasible dual minimization value. Equality is guaranteed only under suitable optimality conditions, not for every feasible pair.
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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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