Answered: In a previous exercise, you were asked…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

In a previous exercise, 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, 40% will return to the Airport, and 20% will be at Oficina Vallejo. Similarly, 70% of the Oficina Vallejo cars will end up Downtown, with 10% returning to Oficina Vallejo and 20% 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.

Let A_n, V_n, and D_n 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 A_n, V_n, and D_n each as functions of A_n − 1, V_n − 1, and D_n − 1.