1. The problem statement, all variables and given/known data A feasible dictionary whose last row reads z = z* + ∑ cjxjdescribes an optimal solution if and only if cj ≤ 0 for all j. Prove or disprove. 2. Relevant equations 3. The attempt at a solution It is clear that if all c's are ≤ 0, then the solution is optimal since increasing any of the variables would either lower or not affect the value of the objective function. The opposite direction does not seem like it would be true, but I have no idea how to start proving that.