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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?

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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.

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