7. A company is considering using Markov theory to analyse consumers switching between the five different brands of washing aids which it markets. All of these washing aids are designed to make washed clothes clean and fresh, but use different approaches. Two of these aids (A and B), are powder based. A further two (C and D), are based on liquid filled tablets. The final aid (E) is just liquid based. The current market shares for the five washing aids are 10%, 20%, 35%, 25% and 10% for aids A,B,C,D and E respectively. Market research has produced the data shown below for the probability of customers switching between washing aids every six months. To washing aid A B C D E From A 1 0 0 0 0 washing B aid 0.37 0.17 0.07 0.39 0 C 0 0 1 0 0 D 0.38 0.20 0.13 0.29 0 E 0 0 0 1 0 Here, for example, there is a probability of 0.07 that a customer switches from aid B to aid C. (a) Copy the following table into your answer and fill in the market shares for these brands after six months. A B C D E Market share (%, 2dp)

7. A company is considering using Markov theory to analyse consumers switching between the five different brands of washing aids which it markets. All of these washing aids are designed to make washed clothes clean and fresh, but use different approaches. Two of these aids (A and B), are powder based. A further two (C and D), are based on liquid filled tablets. The final aid (E) is just liquid based. The current market shares for the five washing aids are 10%, 20%, 35%, 25% and 10% for aids A,B,C,D and E respectively. Market research has produced the data shown below for the probability of customers switching between washing aids every six months. To washing aid A B C D E From A 1 0 0 0 0 washing B aid 0.37 0.17 0.07 0.39 0 C 0 0 1 0 0 D 0.38 0.20 0.13 0.29 0 E 0 0 0 1 0 Here, for example, there is a probability of 0.07 that a customer switches from aid B to aid C. (a) Copy the following table into your answer and fill in the market shares for these brands after six months. A B C D E Market share (%, 2dp)

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 9EQ

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