Define the states and state space of the markov chain

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Assignment:

A product manager (PM) at the head office of supermarket chain makes some analysis about chips sales. In their supermarket chains they provide three brand names for chips. After analysing purchasing records, PM discovers that every week: BrandA chips lose 12%of its customers who change to BrandB chips, and that 19%purchase BrandC chips. BrandB chips lose 16%of its customers who buy BrandA chips, and 10%of its customers who buy BrandC chips; BrandC chips lose 20%of its customers who buy BrandA and 14%who purchase BrandB. Let us assume that this week 750 people buy BrandA, 700 consume BrandB and 1,000 purchase BrandC.

(a) Define the states and state space of the markov chain.

(b) Provide the state transition matrix. Show all your calculations

(d) How many customers will buy BrandC chips in 2 week's time?

(e) After a given time, what proportion of people will buy the BrandA, BrandB and BrandC chips?

Reference no: EM133339798

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