Formulate, but do not solve, the Linear Programming model which minimizes total shipping costs for the question below. Note: Skateboards can only be shipped in whole units (not in fractional units). (20 pts.)
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 two distribution centers, or DCs (located in Iowa and Maryland).
Skateboards are then shipped from the distribution centers to three major U.S. retailers: Just Sports, Sports ‘N Stuff and The Sports Dude. The weekly demands are 250 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 the DCs and for shipping between the DCs and the retailers.
Shipping Costs ($ per skateboard)
Factory / DCs? Iowa Maryland
Detroit $2.50 $2.50
Los Angeles $3.50 $4.50
Austin $4.00 $4.00
Shipping Costs ($ per skateboard)
Retailers / DCs? Iowa Maryland
Just Sports $3.00 $2.00
Sports ‘N Stuff $2.75 $3.25
The Sports Dude $3.00 $4.00