DO THIS PROBLEM USING EXCEL Solver and generate the reports to answer the questions below

American Eagle promotes body positivity and self love. Because being yourself is a primary message for the company, many employees want to add more variety to jeans. Option $A$ is to add more sizes to the jeans sold while option B is to add more of a variety of fits $($short$,$ long, curvey etc$).$ Option A requires $40$ pounds of a material, $80$ minutes of design time, and $120$ minutes of manufacturing time. Option B requires $50$ pounds of material, $200$ minutes of design time, and $80$ minutes of manufacturing time. American Eagles supplier indicated that at most $80,000$ pounds of jean materials will be available next quarter. In addition, American Eagles estimates that $4000$ hours of design time and $3200$ hours of manufacturing time will be available next quarter. The profit contributions are $$400$ per unit for option A and $$480$ per unit for Option B$.$

A$)$ Define the mathematical model for this problem and develop an excel model using $$ solver.

B$)$ What is the optimal solution and the total profit contribution?

$$ C$)$ How much unused capacity does manufacturing minutes have at the optimal solution?

$4$

D$)$ If the supplier offered to provide American Eagle with an additional $1000$ pounds of $$ material, should American Eagle purchase the additional pounds of jean material? Explain.

E$)$ Because of increased competition, American Eagle is considering reducing the price of A such that the new contribution to profit is $$350$ per unit. How would this change in price affect the optimal solution? Explain.