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 one of 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. 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 skateboards between the DCs and the retailers. Shipping Costs (per skateboard) Factory to DCFactory/DCs Iowac Maryland Idaho ArkansasDetroit $25.00 $25.00 $35.00 $40.00Los Angeles $35.00 $45.00 $35.00 $42.50Austin $40.00 $40.00 $42.50 $32.50 Shipping Costs (per skateboard) DC to RetailerRetailers/DCs Iowa Maryland Idaho ArkansasJust Sports $30.00 $20.00 $35.00 $27.50Sports 'N Stuff $27.50 $32.50 $40.00 $25.00The Sports Dude $30.00 $40.00 $32.50 $42.50a) Develop a production and shipping schedule for Sports of All Sorts. b) What is the minimal transportation cost?c) Sports of All Sorts is considering expansion of the Iowa Distribution Center to 800 units per week. The annual amortized cost of expansion is $40,000. Should the company expand the Iowa DC capacity so that it can process 800 skateboards per week? Assume there are 50 operating weeks a year. Hint: run the problem again assuming 800 units in Iowa, determine the weekly change in costs, and multiply by 50 for annual cost changes.