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A supermarket sells three types of salads: Arugula, Baby Kale, and Spring Mix. Every week, 40% of the people who bought Arugula last week switch to Baby Kale, 20% switch to Spring Mix, and 40% buy Arugula again. Similarly, 20% of customers who bought Baby Kale last week switch to Arugula, 10% switch to Spring Mix and the remaining 70% buy Baby Kale again. Those who bought Spring Mix last week, 20% switch to Arugula, 20% switch to Baby Kale, and 60% stay with Spring Mix. (a) (b) after two weeks. (Be careful when multiplying decimals, 0.2 - 0.2 = 0.04.) (c) Find the transition matrix of the corresponding random walk. Find the probability that a Spring Mix buyer will buy Spring Mix again In the long run, what will the share of each type of salad be? Give the answer as a probability vector.

A supermarket sells three types of salads: Arugula, Baby Kale, and Spring Mix. Every week, 40% of the people who bought Arugula last week switch to Baby Kale, 20% switch to Spring Mix, and 40% buy Arugula again. Similarly, 20% of customers who bought Baby Kale last week switch to Arugula, 10% switch to Spring Mix and the remaining 70% buy Baby Kale again. Those who bought Spring Mix last week, 20% switch to Arugula, 20% switch to Baby Kale, and 60% stay with Spring Mix. (a) (b) after two weeks. (Be careful when multiplying decimals, 0.2 - 0.2 = 0.04.) (c) Find the transition matrix of the corresponding random walk. Find the probability that a Spring Mix buyer will buy Spring Mix again In the long run, what will the share of each type of salad be? Give the answer as a probability vector.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 3EQ: A florist offers three sizes of flower arrangements containing roses, daisies, and chrysanthemums....
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A supermarket sells three types of salads: Arugula, Baby Kale, and Spring Mix. Every week, 40% of the people who bought Arugula last week switch to Baby Kale, 20% switch to Spring Mix, and 40% buy Arugula again. Similarly, 20% of customers who bought Baby Kale last week switch to Arugula, 10% switch to Spring Mix and the remaining 70% buy Baby Kale again. Those who bought Spring Mix last week, 20% switch to Arugula, 20% switch to Baby Kale, and 60% stay with Spring Mix. (a) (Б) after two weeks. (Be careful when multiplying decimals, 0.2 - 0.2 = 0.04.) (c) Find the transition matrix of the corresponding random walk. Find the probability that a Spring Mix buyer will buy Spring Mix again In the long run, what will the share of each type of salad be? Give the answer as a probability vector.
Transcribed Image Text:A supermarket sells three types of salads: Arugula, Baby Kale, and Spring Mix. Every week, 40% of the people who bought Arugula last week switch to Baby Kale, 20% switch to Spring Mix, and 40% buy Arugula again. Similarly, 20% of customers who bought Baby Kale last week switch to Arugula, 10% switch to Spring Mix and the remaining 70% buy Baby Kale again. Those who bought Spring Mix last week, 20% switch to Arugula, 20% switch to Baby Kale, and 60% stay with Spring Mix. (a) (Б) after two weeks. (Be careful when multiplying decimals, 0.2 - 0.2 = 0.04.) (c) Find the transition matrix of the corresponding random walk. Find the probability that a Spring Mix buyer will buy Spring Mix again In the long run, what will the share of each type of salad be? Give the answer as a probability vector.
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