Break down the calculations using Excel $-$ Polly Astaire makes fine clothing for big and tall men. A few years ago, Astaire entered the sportswear market with the Sunset line of shorts, pants, and shirts. Management wants to make the amount of each product that will maximize profits. Each type of clothing is routed through two departments, A and B$.$ The relevant data for each product are as follows:

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Department A has $120$ hours of capacity; department B has $160$ hours of capacity and $90$ yards of material area is available. Each shirt contributes $$10$ to profits and overhead; each pair of shorts, $$10$; and each pair of pants, $$23.$

a$.$ Specify the objective function and constraints for this problem.

B$.$ Use a computer package such as POM for Windows to solve the problem.

c$.$ How much should Astaire be willing to pay for an extra hour of department A capacity? How much for an extra hour of department B capacity? For what range of right$-$hand values are these shadow prices valid?

PROCESSING TIME $($HR$)$ Product Department A Department B Material $($yd$)$ Shirts $212$ Shorts $231$ Pants $344$