JoJo Jeans makes two kinds of jeans, designer and straight$-$leg. The demand for designer jeans $($x$1)$ and straight$-$leg jeans $($x$2)$ are defined by the demand relations:

x$1=150024\mathrm{.}6$p$1$ and x$2=270063\mathrm{.}8$p$2,$ where p$1$ and p$2$ represent the price of each jean type.

The cost of producing designer jeans is $$12$ per pair, and the cost of producing straight$-$leg is $$9$ per pair.

The production of jeans is subject to the following resource constraints for cloth, cutting time, and sewing time in the form:

Cloth $2$x$1+2\mathrm{.}7$x$2<=6000$ yards

Cutting $3\mathrm{.}6$x$1+2\mathrm{.}9$x$2<=8500$ minutes

Sewing $7\mathrm{.}2$x$1+8\mathrm{.}5$x$2<=15,000$ minutes

$10$ points $$ Develop in Excel, and use the Solver tool, the solution to the nonlinear programming problem where the firm would like to maximize the profit across jean types subject to its constraints. Submit your Excel file where you retain the sheet where you develop the model and include the Answer report as a separate sheet.

$10$ points for the next $4$ questions $(2\mathrm{.}5$ each$).$

What is the maximum profit attainable given the constraints?

What are the values for x$1$ and x$2$ at the maximum profit?

What are the values for p$1$ and p$2$ at the maximum profit?

Are any of the resource constraints binding?