Final answer:
The optimal value of the objective function may either remain the same or increase when the feasible region gets larger, depending on the specific problem and its constraints.
Step-by-step explanation:
When the feasible region gets larger due to a change in one of the constraints, the optimal value of the objective function may either remain the same or increase. It depends on the specific situation and the relationship between the objective function and the constraints.
For example, imagine a linear programming problem where the objective function represents profit, and the constraints represent resource limitations. If a constraint is relaxed or expanded, it could allow for more resources to be allocated, potentially increasing the profit. However, if the objective function already reaches its maximum value within the original feasible region, then the optimal value would remain the same.
In summary, the optimal value of the objective function can either remain the same or increase when the feasible region gets larger, depending on the specific problem and its constraints.