Problem #2: Rick Eldridge is the new Vice President for operations at The Golfers Link (TGL), a company specializing in the production of quality, discount sets of golf clubs. Rick was hired primarily because of his expertise in supply chain management (SCM). SCM is the integrated planning and control of all resources in the logistics process from the acquisition of raw materials to the delivery of finished products to the end user. Because SCM seeks to optimize all activities in the supply chain including transactions between firms, Ricks first priority is ensuring that all aspects of production and distribution within TGL are operating optimally. TGL produces three different lines of golf clubs for men, women, and junior golfers at manufacturing plants in Daytona Beach, FL, Memphis, TN, and Tempe, AZ. The plant in Tempe produces all three lines of clubs. The one in Daytona produces only the mens and womens lines, and the plant in Memphis produces only the womens and juniors lines. Each line of clubs requires varying amounts of three raw materials that are sometimes in short supply: titanium, aluminum, and a distinctive rock maple wood that TGL uses in all of its drivers. Thus, the amount of each of these materials required in each set of the different lines of clubs is summarized below: Resources Required per Club Set (in lbs) Men's Women's Juniors' Titanium 2.9 2.7 2.5 Aluminum 4.5 4 5 Rock Maple 5.4 5 4.8 The estimated amount of each of these key resources available at each plant during the coming month is given as: Estimated Resource Availability (in lbs) Daytona Memphis Tempe Titanium 4500 8500 14500 Aluminum 6000 12000 19000 Rock Maple 9500 16000 18000 TGLs reputation for quality and affordability ensures that it can sell all the clubs it can make. The mens, womens, and juniors lines generate wholesale revenues of $225, $195, and $165 respectively, regardless of where they are produced. Club sets are shipped from the production

plants to distribution centers in Sacramento, CA, Denver, CO, and Pittsburg, PA. Each month, the different distribution centers order the number of club sets in each of the three lines that they would like to receive. TGLs contract with this distributor requires filling at least 90% (but no more than 100%) of all distributor orders. Rick recently received the following distributor orders for the coming month: Number of Club Sets Ordered Men's Women's Juniors' Sacramento 700 900 900 Denver 550 1000 1500 Pittsburgh 900 1200 1100 The cost of shipping a set of clubs to each distribution point from each production facility is summarized in the following table. Note again that Daytona does not produce juniors club sets and Memphis does not produce mens club sets. Shipping Costs Men's Women's Juniors' To/From Daytona Tempe Daytona Memphis Tempe Memphis Tempe Sacramento $51 $10 $49 $33 $9 $31 $8 Denver $28 $43 $27 $22 $42 $21 $40 Pittsburgh $36 $56 $34 $13 $54 $12 $52 Rick has asked you to determine an optimal production and shipping plan for the coming month. Part a. Formulate an LP for this problem. (15 points) Part b. Create a spreadsheet model for this problem in EXCEL and solve it. What is the optimal solution? (The optimal objective function value is $1,304,544.25) (10 points) Part c. If Rick wanted to improve the solution, what additional resources would be needed and where would they be needed? Explain, referring to the shadow prices for each of the resource constraints. (10 points) Part d. How would the solution change if the men's, women's and juniors' lines generated wholesale revenues of $255, $195 and $175 instead? By how much could the revenues generated for each of the products be increased without changing the optimal solution to the original problem? (5 points) Part e. Are there any alternate optimal solutions? Explain. (5 points)