A regional rent-a-car company has offices in Lincoln, Omaha and ten other small cities. Their records show that each week, 55% of the cars rented in Lincoln returned to Lincoln, 35% are returned to Omaha and the remaining cars are returned elsewhere. Of those rented in Omaha, 75% are returned to Omaha, 5% to Lincoln and 20% elsewhere. Of the cars rented in the ten other cities, 25% are returned to Omaha and 5% to Lincoln. (a) Draw a graph illustrating the states and the transition rates. (b) Set up a linear dynamical system which models this situation. Simulate your system using python. Start with 100% of the cars in Lincoln, and output the fraction of the cars in each of Lincoln, Omaha and elsewhere each week; (c) Compute the steady state analytically