What is the linear programming model for this problem? $($Assume R is the number of units of regular model gloves and C is the number of units of catcher's model gloves.$)$

Recall that the firm has $850$ hours of production time available in its cutting and sewing department, $200$ 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 in the following table.

Model Production Time

$($hours$)$

Cutting and Sewing Finishing Packaging and

Shipping Profit$/$Glove

Regular model $1$

$1$

$2$

$1$

$8$

$$4$

Catcher's model

$3$

$2$

$1$

$3$

$1$

$4$

$$7$

The full model that will be used to solve linear programming problems is made up of an objective function and constraints. The objective function is an expression that will be minimized or maximized. Constraints are equations or inequalities that mathematically describe the limitations of the variables. Watch the video to learn how to create the linear programming model for this problem. Note that the data in the video is not the same as what is given for this problem, but the process remains the same.