A retailer stocks three brands of breakfast cereal. A survey is taken of 5000 people who purchase

Question:

A retailer three brands of breakfast cereal. A survey is taken of 5000 people who purchase cereal weekly from this retailer. Each week, Crispy Flakes loses 12% of its customers to Crunchy Nuggets and 19% to Toasty Cinnamon Twists. Crunchy Nuggets loses 16% of its customers to Crispy Flakes and 10% of its customers to Toasty Cinnamon Twists, and Toasty Cinnamon Twists loses 20% of its customers to Crispy Flakes and 14% to Crunchy Nuggets.
(a) Set up a stochastic matrix displaying these transitions.
(b) Suppose that, this week, 1500 people buy Crispy Flakes, 1500 buy Crunchy Nuggets, and 2000 people buy Toasty Cinnamon Twists. How many people will buy Crispy Flakes next week? How many will buy Toasty Cinnamon Twists in two weeks?
Stocks
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