Kelson Sporting Equipment, Inc., makes two different types f 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 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 Regular model Catcher's model Production Time (hours) Cutting Packaging and Sewing Finishing and Shipping 1/2 1/4 3/2 1/2 1/2 Profit/Glove $8 $12 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? If your answer is zero, enter "0". If you need a negative number, enter minus sign with it. If necessary, enter the numbers as a common fraction. If the constant is "1" it must be entered in the box. Let R = number of units of regular model. C = number of units of catcher's model. Max R c s.t. R+ 10 10 10 RC Cutting and sewing Finishing Packaging and Shipping b. Select the correct graph that reflects the optimal solution. The optimal solution will state how many gloves of each model Kelson should manufacture. (0) (ii) 1000 1000 900 900 800 800 700 700 +....Optimal Solution (0.600) 600 600 Catcher's Model Catcher's Model 500 500 400 400 + C&S C&s 300 300 200+ 200 F P&S P&S F 100 100 Optimal Solution (6000 100 200 300 400 500 600 700 800 900 1000 100 200 300 400 500 600 700 800 900 1000 Regular Model Regular Model (iii) (iv) 1000 1000 900 900 800 800 700 700 600 600 Catcher's Model Catcher's Model 500 500 400 C&S 400 C&S 300 300 F 200 F 200 P&S 100 Optimal Solution 19000) 100 P&S Optimal Solin (400,0) R 100 200 300 400 500 600 700 800 900 1000 Regular Model 100 200 300 400 500 600 700 800 900 1000 Regular Model c. What is the total profit contribution Kelson can earn with the given production quantities? If required, round your answer to the nearest dollar. $ d. How many hours of production time will be scheduled in each department? If required, round your answer to the nearest whole number. C&S TI P&S e. What is the slack time in each department? If required, round your answer to the nearest whole number. If no entry is required, enter "o". Department Capacity Usage Slack C&S hours F hours P&S hours