When a constraint is removed from a linear programming (LP) problem, it can have the following effects:
(a) The feasible region:
The feasible region is the set of all possible solutions that satisfy the constraints of the LP problem. When a constraint is removed, the feasible region typically expands, as there are fewer restrictions on the possible solutions. In some cases, removing a constraint may have no effect on the feasible region if the removed constraint did not impact the original feasible region.
(b) The optimal value of the objective function:
Since the feasible region expands when a constraint is removed, it is possible that a new, better solution may become available. This can potentially increase the optimal value of the objective function, especially in a maximization problem.
However, it is also possible that the optimal value remains the same if the removed constraint did not affect the original optimal solution. In other words, if the optimal solution found in the original problem still lies within the expanded feasible region and no better solution is available, the optimal value of the objective function will not change.
Removing a constraint from a linear programming problem can result in an expanded feasible region and may lead to an increased optimal value of the objective function in a maximization problem. However, it is also possible that the optimal value remains unchanged if the removed constraint did not impact the original optimal solution.