I'm struggling with this question. I understand that with the strong duality theorem, the dual LP is infeasible when primal is unbounded (ex: linear programming infeasibility, dual & primal relation).
My intuition tells me this is false, but I'm having trouble coming up with an example to prove it. Any pointers?
Best Answer
Consider the linear programming problem of $$\min c^Tx$$ subject to $$Ax=b.$$
where $ A=0, c=b=1$ and $x \in \mathbb{R}$.
Verify that both the primal and the dual are infeasible.