The Easy Drive Car Rental Agency needs 500 new cars in its Nashville operation and 300 new cars in Jacksonville, and it currently has 400 new cars in both Atlanta and Birmingham. It costs $30 to move a car from Atlanta to Nashville, $70 to move a car from Atlanta to Jacksonville, $40 to move a car from Birmingham to Nashville, and $60 to move a car from Birmingham to Jacksonville. The agency wants to determine how many cars should be transported from the agencies in Atlanta and Birmingham to the agencies in Nashville and Jacksonville in order to meet demand while minimizing the transport costs. Develop a mathematical model for this problem and use logic to determine a solution.