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 Towa, 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 Idaho LE Arkansas LZ Detroit L1 25.00 25.00 35.00 40.00 Los Angeles 2 35.00 45.00 35.00 42.50 Austin 40.0 40.0 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 5 Idaho Arkansas Just Sports Lg 30.00 20.00 35.00 27.50 Sports 'N Stuff L9 27.50 32.50 40.00 25.00 The Sports Dude 30.00 40.00 32.50 42.50 () Draw the network representation for this problem. (Submit a file with a maximum size of 1 MB.) Choose File ] No file chosen Network representation.jpg Score: 0.83 out of 0.83 Comment: (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 / to node j.) 24x- 425145 + 35x16 + 40x17 + 35X24 + 45X25 + 35x28 + 42.5x27 + 4034 + 40x45 + 42.5x36 + 32.5x37 - Min(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 / to node j.) Min 24x- 425X15 + 35x16 + 40x17 + 35X24 + 45x25 + 35x26 + 42.5x27 + 40x34 + 40x45 + 42.5x36 + 32.5x37 - s.t Detroit Production X14 + *15 + X16 + X - : 200 Sports Stuff Demand X49 + X59 + X69 + X79 = 500 Sports Dude Demand *410 + *510 + *610 + *710 2 650 x 2 0 for all i and j