Linear programming, could I get some help

11. Recall the Kelson Sporting Equipment problem (Chapter 2, Problem 22). Letting R = number of regular gloves C = number of catcher's mitts leads to the following formulation: Max 5R+ 8C SJ. R + %C s 900 Cutting and sewing 53R + 14c 5 300 Finishing 1A\"? + 'AC 5 100 Packaging and shipping R, C 2 0 The computer solution obtained using The Management Scientist is shown in Figure 3.13. FIGURE 3. 13 THE MANAGEMENT SCIENTIST SOLUTION FOR THE KBLSON SPORTING EQUIPMENT PROBLEM % Objective Function Value = 3'?00 . 00150 Variable Value Reduced Costs R 500.00150 0 00000 C 149. 99925 0 00000 Constraint slack/Surplus Dual Prices 1 1?4 . 99963 0 00000 2 0.00000 2.99999 3 0.00000 23.00006 OBJECTIVE COEFFICIENT RANGES Variable Lower Limit Current Value Upper Limit R 4.00000 5.00000 12.00012 C 3.33330 ' 8.00000 10.00000 RIGHT HAND SIDE RANGES Constraint Lower Limit Current Value Upper 1111010 1 T25 . 0003'? 900 . 00000 No Upp'er Limit 2 133.33200 300.00000 400.00000 3 75 . 00000 100 . 00000 134 . 99902 a. What is the optimal solution, and what is the value of the total prot contribution? b. Which constraints are binding? c. What are the dual prices for the resources? Interpret each. d. If overtime can be scheduled in one of the departments, where would you recom mend doing so? Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: :1 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 nishing department, and 100 hours available in its packaging and shipping department. The production time requirements and the prot contribution per glove are given in the following table. Production Time {hours} Cutting I Packaging Model and Sewing Finishing and Shipping Prot fGIove Regular model 1 1/2 1/5 $5 Catcher's model 3/3 1/3 1/4 $8 Assuming that the company is interested in maximizing the total prot contribution, an swer the following: a. What is the linear programming model for this problem? 1). Find the optimal solution using the graphical solution procedure. How many gloves of each model should Kelson manufacture? c. What is the total prot contribution Kelson can earn with the listed production quantities