A car rental agency has offices in Phoenix, Denver, Chicago, and Atlanta. The agency allows one- and two-way rentals so that cars rented in one location may end up in another. Statistics show that at the end of each week 70% of all rentals are two way. As for the one-way rentals: From Phoenix, 20% go to Denver, 60% to Chicago, and the rest goes to Atlanta; from Denver, 40% go to Atlanta and 60% to Chicago; from Chicago, 50% go to Atlanta and the rest to Denver; and from Atlanta, 80% go to Chicago, 10%

to Denver, and 10% to Phoenix.

(a) Express the situation as a Markov chain.

(b) If the agency starts the week with 100 cars in each location, what will the distribution be like in two weeks?

(c) If each location is designed to handle a maximum of 110 cars, would there be a long-run space availability problem in any of the locations?

(d) Determine the average number of weeks that elapse before a car is returned to its originating location.