Consider the isolated Swiss town of Andelfingen, inhabited by 1200 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 Wipf's the following week. The state of this town (as far as grocery shopping is concerned) can be represented by the vector x( m(t) where w(t) and m(t) are the numbers of families shopping at Wipf's and at Migros, respectively, t weeks after Migros opens. Suppose w(0) = 1200 and m(0) = 0. A. Find a 2 x 2 matrix A such that x(t + 1) = Ax(t). B. How many families will shop at each store after t weeks? Give closed formulas. C. The Wipfs expect that they must close down when they have fewer than 250 customers a week. When does that happen?
Consider the isolated Swiss town of Andelfingen, inhabited by 1200 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 Wipf's the following week. The state of this town (as far as grocery shopping is concerned) can be represented by the vector x( m(t) where w(t) and m(t) are the numbers of families shopping at Wipf's and at Migros, respectively, t weeks after Migros opens. Suppose w(0) = 1200 and m(0) = 0. A. Find a 2 x 2 matrix A such that x(t + 1) = Ax(t). B. How many families will shop at each store after t weeks? Give closed formulas. C. The Wipfs expect that they must close down when they have fewer than 250 customers a week. When does that happen?
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
Related questions
Question
Show all your work
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 4 images
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Expert Answers to Latest Homework Questions
Q: None
Q: help please answer in text form with proper workings and explanation for each and every part and…
Q: help please answer in text form with proper workings and explanation for each and every part and…
Q: help please answer in text form with proper workings and explanation for each and every part and…
Q: help please answer in text form with proper workings and explanation for each and every part and…
Q: help please answer in text form with proper workings and explanation for each and every part and…
Q: None
Q: None
Q: None
Q: None
Q: help please answer in text form with proper workings and explanation for each and every part and…
Q: help please answer in text form with proper workings and explanation for each and every part and…
Q: help please answer in text form with proper workings and explanation for each and every part and…
Q: None
Q: help please answer in text form with proper workings and explanation for each and every part and…
Q: None
Q: help please answer in text form with proper workings and explanation for each and every part and…
Q: help please answer in text form with proper workings and explanation for each and every part and…
Q: None
Q: None
Q: help please answer in text form with proper workings and explanation for each and every part and…