This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher's model. The firm has $830$ 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 $11218$ $$8$ Catcher's model $321314$ $$9$ 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? $($Assume R is the number of units of regular model gloves and C is the number of units of catcher's model gloves.$)($b$)$ Develop a spreadsheet model and find the optimal solution using Excel Solver. How many of each model should Kelson manufacture? $($c$)$ What is the total profit contribution $($in dollars$)$ Kelson can earn with the optimal production quantities? $($d$)$ How many hours of production time will be scheduled in each department? $($e$)$ What is the slack time $($in hours$)$ in each department? 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.$)$ Recall that the firm has $830$ 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 $11218$ $$8$ Catcher's model $321314$ $$9$ 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. Let R be the number of units for regular model gloves and C be the number of units for catcher's model gloves. Give the objective function that will be maximized and the constraints. Max s$.$t$.$ cutting and sewing finishing packaging and shipping R$,$ C $>=0$