Suppose a linear programming (maximization) problem has been solved and the optimal value of the objective function is $300. Suppose a constraint is removed from this problem
Explain how this might affect each of the following:
(a) the feasible region.
(b) the optimal value of the objective function.
(a) Removing a constraint may, if the constraint is not redundant, increase the size of the feasible region. It can never make the feasible region any smaller. If the constraint was active in the solution, removing it will also result in a new optimal solution. However, removing an essential constraint could cause the problem to become unbounded.
(b) Removal of a constraint can only increase or leave the same the size of the feasible region; therefore, the value of the objective function will either increase or remain the same, assuming the problem has not become unbounded.
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