Discussion
For a linear programming problem, which one of the following statements is FALSE?
Answer: D
The FALSE statement is Even if both primal and dual are feasible, the optimal values of the primal and the dual can differ.
By the strong duality theorem, if both the primal and the dual are feasible, both have optimal solutions and their optimal objective values are equal. So the values cannot differ.
The other three are true. An equality constraint in the primal gives a dual variable unrestricted in sign. Both problems can be infeasible at once; standard small examples exist. And by weak duality, an unbounded primal leaves no feasible point for the dual, since any dual feasible value would bound the primal.
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