Final answer:
Changes within the allowable range of an objective function coefficient will not affect the optimal solution, as this range defines the values over which the current solution remains optimal.
Step-by-step explanation:
When a change in the value of an objective function coefficient remains within the allowable range, the optimal solution will also remain the same. This is because the allowable range for an objective function coefficient is the range of values over which the current basis (i.e., the set of variables that provide the optimal solution) remains optimal. If the coefficient changes within this range, the current solution continues to be the best one. It's important to always check the answer to see if it's reasonable, considering aspects like proper units, sign, magnitude, and in adherence to physical laws like efficiency being less than 1 and coefficient of performance being greater than 1.