TLG 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, while the one in Daytona only produces Men's and Women's lines, and the plant in Memphis only produces the Women's and Junior's lines. Each line of clubs requires varying amounts of three raw materials, sometimes in short supply: titanium, aluminum, and a distinctive rock maple wood that TGL uses in its drivers. The manufacturing process for each line of clubs at each plant is identical. Thus, the amount of each of these materials required in each set of the different lines of clubs is summarized in the following table: Titanium Aluminum Rock Maple Resources Required per Club Set (in lbs) Men's 2.9 4.5 5.4 Women's 2.7 4 5 Junior's 2.5 5 4.8 The estimated amount of each of these key resources available at each plant during the coming month is given as follows: Estimated Resource Availability (in lbs) Titanium Aluminum Rock Maple Daytona 4,500 6,000 9,500 Memphis 8,500 12,000 16,000 Tempe 14,500 19,000 18,000 TGL's reputation for quality and affordability ensures they can sell all the clubs they can make. The Men's, Women's, and Junior's lines generate wholesale revenue of $225, $195, and $165, respectively, regardless of where they are produced. Club sets are shipped from production plants to Sacramento, CA, Denver, CO, and Pittsburgh, PA, distribution centers. Each month, the different distribution centers order the number of club sets in each of the three lines they would like to receive. TGL's contract with this distributor requires the company to fill at least 90% (but no more than 100%) of all distributor orders. TGL recently received the following distributor orders for the coming month: Sacramento Denver Pittsburgh Resources Required per Club Set (in lbs) Men's 700 550 900 Women's 900 1,000 1,200 Junior's 900 1,500 1,100 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 Junior's club sets, and Memphis does not make Men's club sets. From Men's Women's Junior's To 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 Determine an optimal production and shipping plan for the coming month.