11. In Exercise 23 of Section 2.1, you were asked to model the following scenario with a directed network. A car rental company has three locations in Mexico City: the International Airport, Oficina Vallejo, and Downtown. Customers can drop off their vehicles at any of these locations. Based on prior experience, the company expects that, at the end of each day, 40% of the cars that begin the day at the Airport will end up Downtown, 50% will return to the Airport, and 10% will be at Oficina Vallejo. Similarly, 60% of the Oficina Vallejo cars will end up Downtown, with 30% returning to Oficina Vallejo and 10% to the Airport. Finally, 30% of Downtown cars will end up at each of the other locations, with 40% staying at the Downtown location. This scenario can also be investigated using a discrete-time population model. (a) Let An, Vn, and Dn be the number of cars at the Airport, Oficina Vallejo, and Downtown, respectively, on day n. Write a system of three equations (as in Example 6.23) giving An, Vn, and Dn each as functions of An1, Vn1, and Dn1. (b) Suppose that, initially, A0 = 1000, V0 = 0, and D0 = 0. Use your system to compute A2, V2, and D2. (c) Solve a system of three equations in three variables to find all fixed points of this system. (d) Implement your system on a spreadsheet. Does the rental car population appear to stabilize at a fixed point? This kind of population modelwhere each subpopulation is a linear function of the others and the total population remains constantis called a Markov chai