Please let me know if my answer is correct for the question below: Question: 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. My answer: If a constraint is removed from a linear programming (LP) problem, it can affect the feasible region and the optimal value of the objective function as follows: (a) The feasible region: Removing a constraint can potentially increase the feasible region of the LP problem. The constraint being removed was previously limiting the values of the decision variables that were feasible. Removing the constraint can allow for a larger range of feasible values for the decision variables and thus expand the feasible region. (b) The optimal value of the objective function: Removing a constraint can potentially change the optimal value of the objective function of the LP problem. If the constraint that is being removed is a binding constraint (i.e., it is active at the optimal solution), removing the constraint could lead to a new optimal solution with a different objective function value. In some cases, removing a constraint may not change the optimal solution or the objective function value if the solution remains feasible and optimal. In summary, removing a constraint from a linear programming problem can potentially affect the feasible region and the optimal value of the objective function. The exact impact will depend on the nature of the constraint being removed and its relationship with the other constraints and objective function.
Please let me know if my answer is correct for the question below:
Question:
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.
My answer:
If a constraint is removed from a linear programming (LP) problem, it can affect the feasible region and the optimal value of the objective function as follows:
(a) The feasible region: Removing a constraint can potentially increase the feasible region of the LP problem. The constraint being removed was previously limiting the values of the decision variables that were feasible. Removing the constraint can allow for a larger range of feasible values for the decision variables and thus expand the feasible region.
(b) The optimal value of the objective function: Removing a constraint can potentially change the optimal value of the objective function of the LP problem. If the constraint that is being removed is a binding constraint (i.e., it is active at the optimal solution), removing the constraint could lead to a new optimal solution with a different objective function value. In some cases, removing a constraint may not change the optimal solution or the objective function value if the solution remains feasible and optimal.
In summary, removing a constraint from a linear programming problem can potentially affect the feasible region and the optimal value of the objective function. The exact impact will depend on the nature of the constraint being removed and its relationship with the other constraints and objective function.
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