Step $1$

$($a$)$ 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.$)$ profit contribution per glove are given in the following table.

$\backslash$table$[[$Model$,\backslash$table$[[$Production Time$],[($hours$)]]],[$Cutting and Sewing,Finishing,$\backslash$table$[[$Packaging and$],[$Shipping$]],$Profit$/$Glove$],[$Regular model,$1,(1)/(2),(1)/(8),$$$7],[$Catcher$\text{'}$s model,$(3)/(2),(1)/(3),(1)/(4),$$$9]]$