lease let me know if my answer is correct the question below: Question 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. please answer so i can cram it easily for the exam My answer: (a) The feasible region: Adding a new constraint can potentially reduce the feasible region of the LP problem. The new constraint could restrict the values of the decision variables that are feasible, which would reduce the feasible region. Alternatively, the new constraint might not affect the feasible region at all if it is redundant or already satisfied by the existing constraints. (b) The optimal value of the objective function: Adding a new constraint can potentially change the optimal value of the objective function of the LP problem. If the new constraint reduces the feasible region, it could reduce the objective function value as well. On the other hand, if the new constraint increases the feasible region, it could improve the objective function value. In some cases, the optimal value may not change at all if the new constraint is redundant or has no impact on the optimal solution.
Please let me know if my answer is correct the question below:
Question
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. please answer so i can cram it easily for the exam
My answer:
(a) The feasible region: Adding a new constraint can potentially reduce the feasible region of the LP problem. The new constraint could restrict the values of the decision variables that are feasible, which would reduce the feasible region. Alternatively, the new constraint might not affect the feasible region at all if it is redundant or already satisfied by the existing constraints.
(b) The optimal value of the objective function: Adding a new constraint can potentially change the optimal value of the objective function of the LP problem. If the new constraint reduces the feasible region, it could reduce the objective function value as well. On the other hand, if the new constraint increases the feasible region, it could improve the objective function value. In some cases, the optimal value may not change at all if the new constraint is redundant or has no impact on the optimal solution.
In summary, adding a new constraint to 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 and its relationship with the existing constraints and objective function.
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