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Consider the isolated Swiss town of Andelfingen, inhabited by 1,200 families. Each

Linear Algebra with Applications | 4th Edition | ISBN: 9780136009269 | Authors: Otto Bretscher ISBN: 9780136009269 434

Solution for problem 28 Chapter 7.2

Linear Algebra with Applications | 4th Edition

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Linear Algebra with Applications | 4th Edition | ISBN: 9780136009269 | Authors: Otto Bretscher

Linear Algebra with Applications | 4th Edition

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Problem 28

Consider the isolated Swiss town of Andelfingen, inhabited by 1,200 families. Each family takes a weekly shopping trip to the only grocery store in town, run by Mr. and Mrs. Wipf, until the day when a new, fancier (and cheaper) chain store, Migros, opens its doors. It is not expected that everybody will immediately run to the new store, but we do anticipate that 20% of those shopping at Wipf s each week switch to Migros the following week. Some people who do switch miss the personal service (and the gossip) and switch back: We expect that 10% of those shopping at Migros each week go to Wipfs the following week. The state of this town (as far as grocery shopping is concerned) can be represented by the vector5(0 =w(t) m(t)where w(t) and m(t) are the numbers of families shopping at Wipfs and at Migros, respectively, t weeks after Migros opens. Suppose w(0) = 1,200 and m(0) = 0. a. Find a 2 x 2 matrix A such that x(t + 1) = Ax(t). Verify that A is a regular transition matrix. (See Exercise 25.) b. How many families will shop at each store after t weeks? Give closed formulas. c. The Wipfs expect that they must close dqwn when they have less than 250 customers a week. When does that happen?

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Chapter 7.2, Problem 28 is Solved
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Textbook: Linear Algebra with Applications
Edition: 4
Author: Otto Bretscher
ISBN: 9780136009269

This textbook survival guide was created for the textbook: Linear Algebra with Applications, edition: 4. The answer to “Consider the isolated Swiss town of Andelfingen, inhabited by 1,200 families. Each family takes a weekly shopping trip to the only grocery store in town, run by Mr. and Mrs. Wipf, until the day when a new, fancier (and cheaper) chain store, Migros, opens its doors. It is not expected that everybody will immediately run to the new store, but we do anticipate that 20% of those shopping at Wipf s each week switch to Migros the following week. Some people who do switch miss the personal service (and the gossip) and switch back: We expect that 10% of those shopping at Migros each week go to Wipfs the following week. The state of this town (as far as grocery shopping is concerned) can be represented by the vector5(0 =w(t) m(t)where w(t) and m(t) are the numbers of families shopping at Wipfs and at Migros, respectively, t weeks after Migros opens. Suppose w(0) = 1,200 and m(0) = 0. a. Find a 2 x 2 matrix A such that x(t + 1) = Ax(t). Verify that A is a regular transition matrix. (See Exercise 25.) b. How many families will shop at each store after t weeks? Give closed formulas. c. The Wipfs expect that they must close dqwn when they have less than 250 customers a week. When does that happen?” is broken down into a number of easy to follow steps, and 222 words. Linear Algebra with Applications was written by and is associated to the ISBN: 9780136009269. Since the solution to 28 from 7.2 chapter was answered, more than 274 students have viewed the full step-by-step answer. This full solution covers the following key subjects: . This expansive textbook survival guide covers 41 chapters, and 2394 solutions. The full step-by-step solution to problem: 28 from chapter: 7.2 was answered by , our top Math solution expert on 03/15/18, 05:20PM.

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Consider the isolated Swiss town of Andelfingen, inhabited by 1,200 families. Each