Cheapest Car Rental rents cars at the Chicago airport. The car rental market consists of two segments: the short$-$term segment, which rents for an average of $0\mathrm{.}5$ week, and the medium$-$term segment, which rents for an average of $2$ weeks. Cheapest currently rents an average of $200$ cars a week to the short$-$term segment and $100$ cars a week to the medium$-$term segment. Approximately $20$ percent of the cars returned $($evenly distributed across both segments$)$ are found to be defective and in need of repairs before they can be made available for rent again. The remaining cars not needing repairs are cleaned, filled with gas, and made available for rent. On average, there are $100$ cars waiting to be cleaned. The average cost of this opera$-$ tion is $$5$ per car. Cars needing repairs spend an aver$-$ age of $2$ weeks in the repair shop and incur an average cost of $$150$ per car. Assume that cars are rented as soon as they are available for rent, that is$,$ as soon as they have been cleaned or repaired. Short$-$term renters pay $$200$ per week, while medium$-$term renters pay $$120$ per week. The flow of cars is shown in Figure $3\mathrm{.}9$ Identify throughput, inventory, and flow time at

each stage.