please show all work and explain steps

that produce skatebosrds. The Detroit and Los Angeles facilities can produce 350 skateboards per week, but the Austin silant is larger and can produce up to 700 skateboards per week. Skatebosrds must be shipped from the factaries to one of four distribution icenters, or DCs (located in lowa, Maryland, Iobho, and Arkansas). Each dstribution center can process (repackage, mark, for sale, and ship) at most 500 skateboardi per week. Skateboards are then shipped from the distribution centers to retallers, 5 ports of Al Sorts supplies three major U.S. retalers: Just: Sports, Sports W Stulf, and The Sports Dude. The weekly demands are 200 skateboards at Just Sports, 500 skateboards at Sperts N 5 tuff, and 650 skateboards at The 5ports Dude. The following (a) Draw the network tepresentation for this problem. (Submit a file with a maximum size of 1 Mb-) No siechoten (b) Bulid a model to minimize the transportation cost of o logistics system that will deliver skateboards from the factorles to the distribution centers and from the Distribution centers to the retallers. (Let Detroit be node 1 , Los Angeles be node 2, Austin be node 3, Jowa be node 4, Marviand 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 xj where x0 represents the number of units shipped from node it to node J.) Min What is the optimal production strategy and shipping pattern for Sports of All Sorts? Enter the number of units shipped where xy represents the number of units shloped from node it to node f. What is the minimum attainable transportation cost (in dollars)? (c) Sports of AI Sorts is considering expansion of the lowa DC capacity to 800 units per week. The annual amortized cost of expanslon is $40,000. Should the Sompany expand the Iona 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 capactly at the lowa distributian center is s per week. Therefoce, the potential savings the potential savings, se Sports of A sorts expand