Consider an LP in standard form, where A 2 Rmn, c 2 Rn, b 2 Rm. Suppose that the set of optimal solutions is bounded. Is it true that all optimal

Consider an LP in standard form, where A 2 Rmn, c 2 Rn, b 2 Rm. Suppose that the set of

optimal solutions is bounded. Is it true that all optimal solutions have at most m nonzeros?

If so, give a proof. If not give a counterexample.