# Linear Programming duality theory

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Let be a given x matrix, and and be given vectors. Use LP duality theory to show that if the problem

has a finite optimal solution, then the following problem

cannot be unbounded, no matter what value might take.

When it says that it has a finite optimal solution, does that mean the problem is infeasible? I am guessing it doesn't so if the first one has an optimal solution then that means the second one has an optimal solution.

If the first one is unbounded then the second cant be unbounded right? But how do I prove that the first one is unbounded? If it even is..

I have no idea how to do this.
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