A manufacturer uses a linear programming model to maximize profit. The objective function coefficient $($OFC$)$ for Product A is $$30.$ Sensitivity analysis shows that the allowable increase for this OFC is $$5,$ and the allowable decrease is $$10.$ If the OFC for Product A changes to $$38,$ what will be the impact on the optimal solution?

The optimal solution will remain the same only if the increase is exactly $$5.$

The optimal solution will change because the increase does not affect the constraints.

The optimal solution will change because the increase exceeds the allowable range.

The optimal solution will remain the same because the increase is within the allowable range.