A car rental agency has offices in Phoenix, Denver, Chicago, and Atlanta. The agency allows in-town and one-way rentals, so that cars rented in one location end up in another. Statistics show that at the end of each week 60% of all rentals are in-town rentals. As for one-way rentals, . From Phoenix, 30% go to Denver, 40% to Chicago, and the rest to Atlanta; . From Denver, 30% go to Atlanta and 70% to Chicago; . From Chicago, 60% go to Atlanta and the rest to Denver; . From Atlanta, 70% go to Chicago, 10% to Denver, and 20% to Phoenix. (a) (50%) Model this operation as a Markov chain and construct the one-step transition matrix (b) (50%) If the company starts the week with 100 cars in each location, what would be the distribution of cars at the end of three weeks