Question: Consider the following Linear Program, max {e r : Ar = b}. (P) Note that this Linear Program is very special, there are no inequalities.

Consider the following Linear Program, max {e r : Ar = b}. (P) Note that this Linear Program is very special, there are no inequalities. (a) Prove that if c is in the row space of A then every feasible solution of (P) is an optimal solution. (b) Prove that if c is not in the row space of A then (P) is infeasible or unbounded. (c) Deduce that (P) is either infeasible, unbounded, or that all feasible solutions are optimal. (d) Give a simple algorithm to solve a Linear Program without inequalities

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