Suppose a linear programming (minimization) problem has been solved and the optimal value of the objective function is $300. Suppose an additional constraint is added to this problem
Explain how this might affect each of the following:
(a) the feasible region,
(b) the optimal value of the objective function.
(a) Adding a new constraint will reduce the size of the feasible region unless it is a redundant constraint. It can never make the feasible region any larger. However, it could make the problem infeasible.
(b) A new constraint can only reduce the size of the feasible region; therefore, the value of the objective function will either increase or remain the same. If the original solution is still feasible, it will remain the optimal solution.
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