Which of the following statements about an LP problem and its dua… - Vidyadip

MCQ

Which of the following statements about an $LP$ problem and its dual is false?

A
If the primal and the dual both have optimal solutions, the objective function values for both problems are equal at the optimum.
B
If one of the variables in the primal has unrestricted sign, the corresponding constraint in the dual is satisfied with equality.
C
If the primal has an optimal solution, so has the dual.
✓
The dual problem might have an optimal solution, even though the primal has no $($bounded$)$ optimum.

✓

Answer

Correct option: D.

The dual problem might have an optimal solution, even though the primal has no $($bounded$)$ optimum.

If one of the problems $($primal, dual$)$ is infeasible then the other problem is infeasible.

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