Answer Happy

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, 10% of the cars that begin the day at the Airport will
end up Downtown, 60% will return to the Airport, and 30%
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, 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.

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.