Chapter 8.2, Problem 21E

Car Rentals The Day-by-Day car rental agency rents cars only on a daily basis. Rented cars can be returned at the end of the day to any of the agency’s three locations—-A, B, or C. Figure 4 shows the percentages of cars returned to each of the locations on the basis of where they were picked up. Assume that all of the agency’s cars are rented each day and that, initially, 40% of the cars are at location A, 30% at location B, and 30% at location C.

Figure 4

a. Set up the stochastic matrix that displays these transitions.

b. Use the matrix from part (a) to estimate the percentage of the cars at location A after one day. After two days.

c. In the long run, what fraction of the cars will be at each location?