Eastern Sporting Equipment, Inc. makes two types of baseball gloves: a regular model and a catcher$$s model. The firm has $900$ hours of production time available in its cutting and sewing department, $300$ hours available in its finishing department, and $100$ hours available in its packaging and shipping department. The production time requirements and the profit contribution per glove are given the following table.

PRODUCTION TIMES PER HOUR MODELS

REGULAR CATCHER

Cutting $11\mathrm{.}5$

Finishing $0\mathrm{.}50\mathrm{.}3$

Packaging and Shipping $0\mathrm{.}1250\mathrm{.}25$

PROFIT $$15$ $$18$

Assuming that the company is interested in maximizing the total profit contribution, answer the following:

a$.$ What is the linear programming $($mathematical$)$ model for this problem?

b$.$ Find the optimal solution using the graphical solution procedure. How many gloves of each model should Eastern Sporting manufacture?

c$.$ What is the total profit contribution Eastern Sporting can earn based on the optimal production quantities?