Discussion
For any primal problem and its dual :
Answer: B
The keyed statement is the primal will have an optimal solution iff the dual does.
This is the fundamental duality theorem of linear programming: if either problem has a finite optimal solution, so does the other, and their optimal objective values are equal.
The other options are not true 'for any' primal problem. Equal optimal values presuppose that optima exist, which fails when the primal is unbounded or infeasible. 'Both primal and dual can not be infeasible' is false: there are pairs in which both are infeasible, for example maximise \(x_{1}\) subject to \(x_{1} - x_{2} \le -1\), \(-x_{1} + x_{2} \le -1\), \(x \ge 0\), whose dual is also infeasible. 'Optimal solution does not exist' is false in general, since most LPs do have optima.
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