Comment by klamike

> A fun fact which is not so difficult to prove in 2 dimensions is that if a linear program has an optimal point (guaranteed when the constraints define a convex polytope), then the minimum objective value will be achieved at one of the vertices of the polytope.

That is, if you assume there is no dual degeneracy :) https://lpviz.net/?s=AsEABN_FCIDiCQC_ixGg4BQAAMCLEYCS9AEAZAA