Sports of All Sorts produces, distributes, and sells high-quality skateboards. Its supply chain consists of three factories (located in Detroit, Los Angeles, and Austin) that produce skateboards. The Detroit and Los Angeles facilities can produce 350 skateboards per week, but the Austin plant is larger and can produce up to 700 skateboards per week. Skateboards must be shipped from the factories to one of four distribution centers, or DCs (located in Iowa, Maryland, Idaho, and Arkansas). Each distribution center can process (repackage, mark for sale, and ship) at most 500 skateboards per week. Shipping Costs ($ per skateboard) Factory /DCs Iowa 4 Maryland 5 Idaho 6 Arkansas Detroit 1 25.00 25.00 35.00 40.00 Los Angeles 12 35.00 45.00 35.00 42.50 3 Austin 40.0 40.00 42.50 32.50 Skateboards are then shipped from the distribution centers to retailers. Sports of All Sorts supplies three major U.S. retailers: Just Sports, Sports 'N Stuff, and The Sports Dude. The weekly demands are 200 skateboards at Just Sports, 500 skateboards at Sports 'N Stuff, and 650 skateboards at The Sports Dude. The following tables display the per-unit costs for shipping skateboards between the factories and DCs and for shipping between the DCs and the retailers. Shipping Costs ($ per skateboard) Retailers/ DCs Iowa 4 Maryland S Idaho 6 Arkansas LZ Just Sports 8 30.00 20.00 35.00 27.50 Sports 'N Stuff 9 27.50 32.50 40.00 25.00 The Sports Dude 30.00 40.00 32.50 12.50 (a) Draw the network representation for this problem. (Submit a file with a maximum size of 1 MB.) (b) Build a model to minimize the transportation cost of a logistics system that will deliver skateboards from the factories to the distribution centers and from the distribution centers to the retailers. (Let Detroit be node 1, Los Angeles be node 2, Austin be node 3, Iowa be node 4, Maryland be node 5, Idaho be node 6, Arkansas be node 7, Just Sports be node 8, Sports Stuff be node 9, and Sports Dude be node 10. Express your answers in the form x; where x; represents the number of units shipped from node i to node j.) Min s.t. Detroit Production Los Angeles Production Austin Production Iowa Shipments Maryland Shipments Idaho ShipmentsArkansas Shipments Iowa Processing Maryland Processing Idaho Processing Arkansas Processing Just Sports Demand Sports Stuff Demand Sports Dude Demand x;; 2 0 for all i and j. What is the optimal production strategy and shipping pattern for Sports of All Sorts? Enter the number of units shipped where x;, represents the number of units shipped from node / to node j. 4 *15 X 17 X24 1 25 X 26 *27 X34 *35 X 37 3 X58 X68 X78 X49 X59 X69 X79 *410 *510 *610 *710] What is the minimum attainable transportation cost (in dollars)? $ (c) Sports of All Sorts is considering expansion of the Iowa DC capacity to 800 units per week. The annual amortized cost of expansion is $40,000. Should the company expand the Iowa DC capacity so that it can process 800 skateboards per week? (Assume 50 operating weeks per year.) The cost of the optimal solution associated with this increased capacity at the Iowa distribution center is $ per week. Therefore, the potential savings over 50 weeks is 50 x ($ = $C per year. The $40,000 cost of expansion ---Select--- the potential savings, so Sports of All Sorts |-Select-- | expand