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, 20% of the cars that begin the day at the Airport will end up Downtown, 70% will return to the Airport, and 10% will be at Oficina Vallejo. Similarly, 60% of the Oficina Vallejo cars will end up Downtown, with 10% returning to Oficina Vallejo and 30% 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 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 D each as functions of An -1, Vn-1, and Dn - 1. An= VN = Dn= X X X
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, 20% of the cars that begin the day at the Airport will end up Downtown, 70% will return to the Airport, and 10% will be at Oficina Vallejo. Similarly, 60% of the Oficina Vallejo cars will end up Downtown, with 10% returning to Oficina Vallejo and 30% 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 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 D each as functions of An -1, Vn-1, and Dn - 1. An= VN = Dn= X X X
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

Transcribed Image Text: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, 20% of the cars that begin the day at the Airport will end up Downtown, 70% will return to the Airport, and 10% will be at Oficina Vallejo. Similarly, 60%
of the Oficina Vallejo cars will end up Downtown, with 10% returning to Oficina Vallejo and 30% 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 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 An
- 1, Vn 1, and Dn - 1.
An =
VN
=
Dn =
X
X
X

Transcribed Image Text: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, 20% of the cars that begin the day the Airport will end up Downtown, 50% will return to the Airport, and 30% will be at Oficina Vallejo. Similarly, 60%
of the Oficina Vallejo cars will end up Downtown, with 10% returning to Oficina Vallejo and 30% to the Airport. Finally, 10% of Downtown cars will end up at each of the other locations, with 80% staying
at the Downtown location.
This scenario can also be investigated using a discrete-time population model.
Consider a system of three equations (as in Example 6.23) giving An, Vn, and Dn each as functions of An-1, Vn - 1, and Dn - 1. Suppose that, initially, Ao = 3000, Vo = 0, and Do = 0. Use your system to
compute A2, V₂, and D₂.
A₂ =
V₂ =
D₂ =
X
X
X
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