Car Rental Co. is concerned about the effect that a newly started cruise line business from the port at Pier-427 will have on its operation. They have discovered that all customers rent from Car Rental's airport location in SD, drive it about 50 miles to Pier-427, and drop it off there. Customers prefer to take the free van service offered by the cruise line to return to the airport at the end of their cruise. Thus, Car Rental has to make arrangements with the local company RailRoad to bring its cars back to the airport location. RailRoad will not allow Hertz to ship more than 500 cars at a time on its trains. Cars arrive at Pier-427 at a constant rate of 100 per day, evenly throughout the day. It costs Hertz $2 per day to park each car at the pier (parking rates are pro-rated depending upon how long a car is parked). Each trip back on the train costs Car Rental a fixed fee of $600, plus a cost of $3 per car on the train. Currently, in order to save on the fixed costs, Hertz waits until there are 500 cars in their parking lot, and then ships them on the train back to the airport. (Assume that CarRental has plenty of extra cars at the airport.)

a. Graphically, show how the number of cars in the parking lot at Pier-427 varies over time under the current system.
b. What is the average number of cars at Pier-427?
c. What is the average total cost per day by Car Rental (in dollars)? Include the amount paid to RailRoad as well as the cost of parking the cars in the lot.
d. What is the optimal number of cars to be shipped back each time?