$1.$ Construct a linear programming model of the supply chain $2.$ Solve the linear programming model you constructed in part $(1).$ What is the total cost? Sports of All Sorts produces, distributes, and sells high$-$quality handcrafted skateboards. Its supply chain consists of three factories that produce the skateboards $($located in Detroit, Los Angeles, and Austin$).$ The Detroit and Los Angeles facilities can produce $35,000$ skateboards per year, but the Austin plant is larger and can produce up to $70,000$ skateboards per year. Skateboards must be shipped from the factories to one of four distribution centers, or DCs$,$ located in Iowa, Maryland, Idaho, and Arkansas. Because of differences in labor rates, the processing and handling charge at each DC is different. These costs per skateboard are $\backslash (\backslash$$ $1\mathrm{.}34\backslash )$ in Iowa, $\backslash (\backslash$$ $1\mathrm{.}62\backslash )$ in Maryland, $\backslash (\backslash$$ $1\mathrm{.}30\backslash )$ in Idaho, and $\backslash (\backslash$$ $1\mathrm{.}38\backslash )$ in Arkansas. Each distribution center can process $($repackage$,$ mark for sale, and ship$)$ at most $50,000$ skateboards per year. 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 following tables display the per unit costs for shipping skateboards between the factories and DCs and for shipping between the DCs and the retailers. Sports of All Sorts needs to forecast the demand at each of its three retail locations for next year, and then plan how to produce and distribute its product from the factories through the DCs to the retailers. The file Skateboards contains five tabs: Plant Capacities, Transportation Costs, DC Capacities, DC Processing Costs, and Historical Demand.