Question: 3. [ 10 points] Consider the problem of minimizing a generic objective function c x where x is constrained to lie inside a standard form

3. [ 10 points] Consider the problem of minimizing a generic objective function cx where x is constrained to lie inside a standard form polyehdron: P={xRn:Ax=b,x0}. Is it true that at every optimal solution of this problem (for any choice of c ), no more than m variables are strictly positive? If your answer is yes, provide a proof or argument. If your answer is no, provide a counterexample.

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