Linear programming : sensitivity analysis and interpretation of solution ( please answer 5 a,b,c,d using figure 8.14... please draw graph wherever needed, thank you)

334 Chapter 8 Linear Programming: Sensitivity Analysis and Interpretation of Solution 5. Refer to the Kelson Sporting Equipment problem (Chapter 7, Problem 24). Letting SELF test R = number of regular gloves C = number of catcher's mitts leads to the following formulation: Max 5R + 80 S.t. R + 3/2C $900 Cutting and sewing 1/2 R + 1/,C $ 300 Finishing 1/3 R + 1/C $ 100 Packaging and shipping R. C20 The sensitivity report is shown in Figure 8.14. a. What is the optimal solution, and what is the value of the total profit contribution? b. Which constraints are binding? C. What are the shadow prices for the resources? Interpret each. d. If overtime can be scheduled in one of the departments, where would you recommend doing so? 6. Refer to the sensitivity information for the Kelson Sporting Equipment problem in SELF test Figure 8.14 (see Problem 5). a. Determine the objective coefficient ranges. Interpret the ranges in part (a). C. Interpret the right-hand-side ranges. d. How much will the value of the optimal solution improve if 20 extra hours of pack- aging and shipping time are made available? 7. Investment Advisors, Ine., is a brokerage firm that manages stock portfolios for a num- ber of clients. A particular portfolio consists of U shares of U.S. Oil and # shares of Huber Steel. The annual return for U.S. Oil is $3 per share and the annual return for FIGURE 8.14 SENSITIVITY REPORT FOR THE KELSON SPORTING EQUIPMENT PROBLEM Variable Cells Model Final Reduced A Rowable Allowable Variable Name Increase Decrease Gloves Standard 500,000 0.000 5.000 7.060 1000 Gloves Deluxe 150,000 0.090 8.000 2.000 1.667 Constraints Final Shadow Constraint Allowable Allowable Same Price R.H.Side Increase Decrease Congo Leaning 2013 Cuning and Dyeing Hours Used 725.000 0.000 900.000 LE + 30 175.000 Finishing Hours Used 300.000 3000 300.090 100.000 166.667 Packinging and Shipping Hours Used 100,000 28:000 100 000 35:000 25.00024. Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular est 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 re- quirements and the profit contribution per glove are given in the following table: Production Time (hours) Cutting Packaging Model and Sewing Finishing and Shipping Profit/ Glove Regular model Catcher's model 3 / 7 $8 Assuming that the company is interested in maximizing the total profit contribution, an- swer the following: What is the linear programming model for this problem? b. Find the optimal solution using the graphical solution procedure. How many gloves of each model should Kelson manufacture? 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? e. What is the slack time in each department