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 DC (located in Iowa, Maryland, Idaho, and Arkansas). Each distribution center can process (repackage, mark for sale, and ship) at most 500 skateboards per week Factory/DCS Shipping Costs (5 per skateboard) Maryland Idaho 6 Arkansas 2 lowa Detroit 0 2 25.00 25.00 35.00 40.00 Los Angeles 35.00 45.00 35.00 42.50 Austin 40 DO 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 Stul, and The Sports Dude. The weekly demands are 200 skateboards at just Sports, 500 skateboards at Sports 'N Stuff, and 650 skateboards at The Sparts 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. Retailers/DCS Shipping Costs (s per skateboard) Maryland Idaho 20.00 35.00 Arkansas 2 Just Sports 27.50 Iowa 4 30.00 27.50 30.00 Sports 'N Stuff 32.50 40.00 25.00 The Sports Dude - 40.00 32.50 42.50 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 , Towabe node 4, Maryland be node 5, Idaho be node , Arkansas be node 7, Nust Sports be made 8, Sports Stull be node 9, and Sports Dude benode 10 Express your answers in the form where x represents the number of units shipped from node to node) Detroit Production Los Angeles Production Austin Production lowa Shipments Maryland Shipments Idaho Shipments Arkansas Shipments towa Processing Meryland Processing Idaho Processing Arkansas Processing Just Sports Demand Sports Stuff Demand Sports Dude Demand X, 20 for all / and What is the optimal production strategy and shipping pattern for Sports of All Sorts? Path Units Cost (5) X14 X510 X09 X610 X78 X79 X710 Totals 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 DC (located in Iowa, Maryland, Idaho, and Arkansas). Each distribution center can process (repackage, mark for sale, and ship) at most 500 skateboards per week Factory/DCS Shipping Costs (5 per skateboard) Maryland Idaho 6 Arkansas 2 lowa Detroit 0 2 25.00 25.00 35.00 40.00 Los Angeles 35.00 45.00 35.00 42.50 Austin 40 DO 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 Stul, and The Sports Dude. The weekly demands are 200 skateboards at just Sports, 500 skateboards at Sports 'N Stuff, and 650 skateboards at The Sparts 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. Retailers/DCS Shipping Costs (s per skateboard) Maryland Idaho 20.00 35.00 Arkansas 2 Just Sports 27.50 Iowa 4 30.00 27.50 30.00 Sports 'N Stuff 32.50 40.00 25.00 The Sports Dude - 40.00 32.50 42.50 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 , Towabe node 4, Maryland be node 5, Idaho be node , Arkansas be node 7, Nust Sports be made 8, Sports Stull be node 9, and Sports Dude benode 10 Express your answers in the form where x represents the number of units shipped from node to node) Detroit Production Los Angeles Production Austin Production lowa Shipments Maryland Shipments Idaho Shipments Arkansas Shipments towa Processing Meryland Processing Idaho Processing Arkansas Processing Just Sports Demand Sports Stuff Demand Sports Dude Demand X, 20 for all / and What is the optimal production strategy and shipping pattern for Sports of All Sorts? Path Units Cost (5) X14 X510 X09 X610 X78 X79 X710 Totals