A company rents moving trucks out of two locations: Detroit and Milwaukee. Some of their customers rent a truck in one city and return it in the other city, and the rest of their customers rent and return the truck in the same city. The company owns a total of 500 trucks. The company has seen the following trend: About 35 percent of the trucks in Detroit move to Milwaukee each week. • About 25 percent of the trucks in Milwaukee move to Detroit each week. Suppose right now Detroit has 330 trucks. If the vector t represents the distribution of trucks, where is the number in Detroit and #2 is ₂ the number in Milwaukee, find the matrix A so that At is the distribution of trucks after 1 week. [Note: You will want to use Sage to complete this problem.] 128 How many trucks will be in each city after 1 week? [Round answers to the nearest whole number.] Detroit: Milwaukee: How many trucks will be in each city after 3 weeks? [Sage makes this one easier. Round answers to the nearest whole number.] Detroit: Milwaukee: Submit Question

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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A company rents moving trucks out of two locations: Detroit and Milwaukee. Some of their customers rent a
truck in one city and return it in the other city, and the rest of their customers rent and return the truck in
the same city. The company owns a total of 500 trucks.
The company has seen the following trend:
About 35 percent of the trucks in Detroit move to Milwaukee each week.
About 25 percent of the trucks in Milwaukee move to Detroit each week.
Suppose right now Detroit has 330 trucks.
[2₁]
If the vector t
represents the distribution of trucks, where 21 is the number in Detroit and 22 is
F2
the number in Milwaukee, find the matrix A so that At is the distribution of trucks after 1 week. [Note:
You will want to use Sage to complete this problem.]
A
How many trucks will be in each city after 1 week? [Round answers to the nearest whole number.]
Detroit:
Milwaukee:
How many trucks will be in each city after 3 weeks? [Sage makes this one easier. Round answers to the
nearest whole number.]
Detroit:
Milwaukee:
Submit Question
Transcribed Image Text:A company rents moving trucks out of two locations: Detroit and Milwaukee. Some of their customers rent a truck in one city and return it in the other city, and the rest of their customers rent and return the truck in the same city. The company owns a total of 500 trucks. The company has seen the following trend: About 35 percent of the trucks in Detroit move to Milwaukee each week. About 25 percent of the trucks in Milwaukee move to Detroit each week. Suppose right now Detroit has 330 trucks. [2₁] If the vector t represents the distribution of trucks, where 21 is the number in Detroit and 22 is F2 the number in Milwaukee, find the matrix A so that At is the distribution of trucks after 1 week. [Note: You will want to use Sage to complete this problem.] A How many trucks will be in each city after 1 week? [Round answers to the nearest whole number.] Detroit: Milwaukee: How many trucks will be in each city after 3 weeks? [Sage makes this one easier. Round answers to the nearest whole number.] Detroit: Milwaukee: Submit Question
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