Kelson Sporting Equipment, Inc., makes two different 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 $400$ 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 $1/21/81$ $$5$

Catcher's model $3/21/41/2$ $$7$

Assuming that the company is interested in maximizing the total profit contribution, answer the following: $($b$)$ Develop a spreadsheet model and find the optimal solution using Solver. How many gloves of each model should Kelson manufacture?

Regular Model $=$

units

Catcher's Model $=$

units

$($c$)$ What is the total profit contribution Kelson can earn with the given production quantities?

$

$($d$)$ How many hours of production time will be scheduled in each department?

Department Production Time $($Hours$)$

Cutting and Sewing

Finishing

Packing and Shipping

$($e$)$ What is the slack time in each department? If your answer is zero, enter $0.$

Department Slack Time $($Hours$)$

Cutting and Sewing

Finishing

Packing and Shipping