Topless City is a small chain of car dealerships that sells vintage convertibles throughout the Southern United States. It is owned and managed by Brandon and Kyle Winslow. Each month Brandon and Kyle attend two car auctions, at which they purchase convertibles: one in Atlanta, the other in Miami. The cars are then shipped to one of three locations: Jackson Mississippi, Birmingham Alabama, or Orlando Florida. There, the cars are refurbished, repainted, safety inspected, and sold at the Topless City dealership in that city. In August, Brandon found 20 cars at the Atlanta auction, and Kyle found 50 cars at the Miami auction which met the needs of the company. Only 15 cars can be worked on at each city during the month, however. Another auction is coming up in September; thus, only 45 cars are to be purchased in August. Topless City wishes to minimize its costs of transporting the cars to the refurbishing locations. The cost to transport cars between cities is shown in the table below.
Jackson Birmingham Orlando
Atlanta $200 $100 $175
Miami $250 $200 $125
b. Formulate the problem as the proper network problem and solve.