The max flow-min cut theorem is one of the most famous theorems of discrete optimization, although it is very straightforward to prove using duality theory from linear programming. Are there any other examples of famous theorems that are also corollaries of LP duality, or duality of convex optimization? The Farkas lemma and the hyperplane separation theorem would be other candidates, although they look more like equivalent statements to me.



Famous theorems that are special cases of linear programming (or convex) duality
To elaborate on M. Winter's comment: Von Neumann's [minimax theorem](https://en.wikipedia.org/wiki/Minimax_theorem) for two-person zero-sum games can be thought of as a consequence of LP duality, although his first proof of the theorem [did not make this connection explicit](https://www.jstor.org/stable/41134130).


