For a maximization problem, adding an additional constraint usually cannot increase the optimal objective value because it reduces or maintains the size of the feasible region, removing some possible solutions rather than creating better ones. The maximum value can only stay the same or decrease. However, the optimal solution point may shift without changing the maximum value if the new constraint removes the original optimal point but another point or an entire edge of the feasible region yields the same objective value. This commonly occurs when there are alternative optimal solutions, where multiple feasible points produce the same maximum value.

Constraint additions, redundancy, and alternate optima are important concepts in graphical linear programming. Constraint additions involve adding new restrictions that may reduce the feasible region, while a redundant constraint is a constraint that does not change the feasible region because it is already satisfied by the other constraints. Alternate optima occur when more than one feasible solution gives the same optimal value, usually when the objective function is parallel to a boundary of the feasible region.