Question

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

Answer 1

The correct option is 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. Hence, the option D is the false statement.