Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher's model. The firm has $800$ hours of production time available in its cutting and sewing department, $300$ hours available in its finishing department, and $250$ hours available in its packaging and shipping department. The production time requirements and the profit contribution per glove are given in the following table:

Production Time $($Hours$)$

Model Cutting and

Sewing

Finishing Packaging and

Shipping

Profit$/$Glove

Regular model $11/21/6$ $$5$

Catcher's model $1/21/41/4$ $$7$

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

$($a$)$ What is the linear programming model for this problem? If required, round your answers to $3$ decimal places or enter your answers as a fraction. If the constant is $"1"$ it must be entered in the box. Do not round intermediate calculation. If an amount is zero, enter $"0".$

Let R $=$ number of units of regular model.

C $=$ number of units of catcher's model.