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The four brands of soap have the current market share of 0.23, 0.28, 0.25, and 0.24 for brands A, B, C, and D, respectively. Below are the transition probability matrix of the soap brands based on their annual performance and the number of customers using the brands. From/To A B C D Number of Customers A 0.2 0.3 0.1 0.4 2300 B 0 0.2 0.5 0.3 2800 C 0.3 0.5 0 0.2 2500 D 0.3 0.4 0.3 0 2400 a) What is the market share of Brand D in the long run? Answer in 2 decimal places. b) How many customers will shift preference in using Brand C soap in the long run? c) What is the mean return time of Brand 1? Answer in 2 decimal places.

The four brands of soap have the current market share of 0.23, 0.28, 0.25, and 0.24 for brands A, B, C, and D, respectively. Below are the transition probability matrix of the soap brands based on their annual performance and the number of customers using the brands. From/To A B C D Number of Customers A 0.2 0.3 0.1 0.4 2300 B 0 0.2 0.5 0.3 2800 C 0.3 0.5 0 0.2 2500 D 0.3 0.4 0.3 0 2400 a) What is the market share of Brand D in the long run? Answer in 2 decimal places. b) How many customers will shift preference in using Brand C soap in the long run? c) What is the mean return time of Brand 1? Answer in 2 decimal places.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.5: Markov Chain
Problem 16E: Consumer Preference In a population of 100,000 consumers, there are 20,000 users of Brand A, 30,000...
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  1. The four brands of soap have the current market share of 0.23, 0.28, 0.25, and 0.24 for brands A, B, C, and D, respectively. Below are the transition probability matrix of the soap brands based on their annual performance and the number of customers using the brands.
    From/To A B C D Number of Customers A 0.2 0.3 0.1 0.4 2300 B 0 0.2 0.5 0.3 2800 C 0.3 0.5 0 0.2 2500 D 0.3 0.4 0.3 0 2400
    a) What is the market share of Brand D in the long run? Answer in 2 decimal places.

    b) How many customers will shift preference in using Brand C soap in the long run?
    c) What is the mean return time of Brand 1? Answer in 2 decimal places.

    d) What is the percentage change of Brand B? Answer in 2 decimal places.
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