8. The leading brewery on the West Coast (labeled A) has hired an OR analyst to analyze its market position. It is particularly concerned about its major competitor (labeled B). The analyst believes that brand switching can be modeled as a Markov chain using three states, with states A and B representing customers drinking beer produced from the aforementioned breweries and state C representing all other brands. Data are taken monthly, and the analyst has constructed the following (one-step) transition matrix from past data. A B C A 0.8 0.25 0.15 B 0.15 0.7 0.05 с 0.05 0.05 0.8 (a) What are the steady-state market shares for the two major breweries? (b) Suppose there are 10 million beer drinking customers. One selling unit of beer costs Brewery A $10 to produce and is sold for $16. For $50 million/year, an advertising firm guarantees to decrease from 15% to 10% the fraction of A customers who switch to B next month, and decrease from 5% to 3% the fraction of A customers who switch to C next month. Should Brewery A hire the advertising firm?
8. The leading brewery on the West Coast (labeled A) has hired an OR analyst to analyze its market position. It is particularly concerned about its major competitor (labeled B). The analyst believes that brand switching can be modeled as a Markov chain using three states, with states A and B representing customers drinking beer produced from the aforementioned breweries and state C representing all other brands. Data are taken monthly, and the analyst has constructed the following (one-step) transition matrix from past data. A B C A 0.8 0.25 0.15 B 0.15 0.7 0.05 с 0.05 0.05 0.8 (a) What are the steady-state market shares for the two major breweries? (b) Suppose there are 10 million beer drinking customers. One selling unit of beer costs Brewery A $10 to produce and is sold for $16. For $50 million/year, an advertising firm guarantees to decrease from 15% to 10% the fraction of A customers who switch to B next month, and decrease from 5% to 3% the fraction of A customers who switch to C next month. Should Brewery A hire the advertising firm?
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Transcribed Image Text:8. The leading brewery on the West Coast (labeled A) has hired an OR analyst to analyze its market
position. It is particularly concerned about its major competitor (labeled B). The analyst believes that
brand switching can be modeled as a Markov chain using three states, with states A and B
representing customers drinking beer produced from the aforementioned breweries and state C
representing all other brands. Data are taken monthly, and the analyst has constructed the following
(one-step) transition matrix from past data.
A
B
с
A
0.8
0.25
0.15
B
0.15
0.7
0.05
с
0.05
0.05
0.8
(a) What are the steady-state market shares for the two major breweries?
(b) Suppose there are 10 million beer drinking customers. One selling unit of beer costs Brewery A
$10 to produce and is sold for $16. For $50 million/year, an advertising firm guarantees to
decrease from 15% to 10% the fraction of A customers who switch to B next month, and
decrease from 5% to 3% the fraction of A customers who switch to C next month. Should
Brewery A hire the advertising firm?
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