Question 3 (20 points). 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 cut- ting and sewing department, 300 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: Production Time (hours) Cutting and Sewing Packaging and Shipping Finishing Model Regular model Profit/Glove $5 1 /2 Catcher's model % $8 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? Define your decision variables and show your objective functions and constraints in your model. b. Find the optimal solution using the graphical solution procedure. Shade the feasible region for this problem. Draw the profit line (objective line) corresponding to a profit of $1600. Move the profit line as far from the origin as you can in order to determine which extreme point will provide the optimal solution. Which constraints are binding? How many gloves of each model should Kelson manufacture? C. What is the total profit contribution Kelson can earn with the given production quantities? How many hours of production time will be scheduled in each department? d What is the slack time in each department? e