If an objective function coefficient changes within its allowable range, the current optimal solution remains optimal. To find the new objective value, substitute the new coefficient into the objective function using the current optimal variable values, then calculate the new total.

If the coefficient change is within its allowable range, the current optimal solution remains valid. Multiply the coefficient change by its variable's optimal value, then add the result to the original objective value to get the new optimal objective value.

You can determine the new optimal objective function value by substituting the changed objective coefficient into the existing optimal solution while keeping the same decision-variable values. As long as the coefficient change stays within its allowable range, the current optimal solution remains optimal, so you simply recalculate the objective function using the new coefficient.