Hello! I'm having trouble with this practice problem. I don't understand why I'm missing some of these.

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answerhappygod
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Hello! I'm having trouble with this practice problem. I don't understand why I'm missing some of these.

Post by answerhappygod »

Hello! I'm having trouble with this practice problem. I don'tunderstand why I'm missing some of these.
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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. Factory/DCs Detroit Los Angeles Austin 1 3 Retailers/DCs Iowa Just Sports Sports 'N Stuff The Sports Dude 25.00 35.00 40.00 8 19 4 10 Shipping Costs ($ per skateboard) 5 Iowa 30.00 27.50 Maryland 30.00 25.00 4 45.00 40.00 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. Maryland 20.00 Idaho 32.50 35.00 40.00 35.00 42.50 Shipping Costs ($ per skateboard) 5 Idaho 35.00 Arkansas 40.00 32.50 40.00 42.50 6 32.50 7 Arkansas 27.50 25.00 42.50 7
(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 where Xij Xij represents the number of units shipped from node i to node j.) Min 25x 14 + 25x15 +35x16 ; +40x17 +35x24 + 45x25 +35x26 + 42.5x27 + 40x34 +40x 45 +42.5x36 +32.5x X
Min 32.5x37 +30x48 +27.5x19 +30x 49 *410 +20x58 +32.5x59 + 40x 510 +35x68 + 40x69 + 32.5x6 610 +27.5x78 ▸ X
27.5x78 +25x79 +42.5x71 *710 X
s.t. Detroit Production 14 +X15+X16 +x17 ≤ 350 Los Angeles Production X24+x25+X26 +*27 ≤ 350 Austin Production *34 +X35+X36 +x37 ≤ 700 Iowa Shipments 14+x24+X34¯X48*49*410* Maryland Shipments X14+x24X34 +x69 -X - X = 0 X48X49 410 -X. Idaho Shipments 14+x24+X34 Arkansas Shipments 14+x24+X34 -X X48*49*410 = 0 Iowa Processing *14+*24+x34≤800 Maryland Processing X15+X25+X35 ≤ 500 Idaho Processing *15+X25+X35 ≤500 Arkansas Processing X17+X27X37 ≤500 Just Sports Demand X48 +X58 +X68 +X78 ≥ 200 Sports Stuff Demand x +x. 49 X59 +x79 ≥ 500 Sports Dude Demand *410X510x610x710 ≥ 650 *48-49 = 0 -X. X "410 = 0 X X X
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