Question: On an average every day, Store A, Store B and Store C get 300, 200 and 150 customers respectively. In Arlington, three grocery stores are

  1. On an average every day, Store A, Store B and Store C get 300, 200 and 150 customers respectively.
  2. In Arlington, three grocery stores are competing each other. Here is the market data for the three grocery stores. Next day (The following information is for transitional probability matrix) a.65% of the customers come back to Store C, 20% of them go to Store A, and 15% of them go to Store b.90% of the Store B customers come back to Store B, 5% of them go to Store A and 5% of them go to store c. 80% of the Store A customers come back to Store A, 15% of them go to Store B and 5% go to store C

Using the above information, calculate the probability of customers (% or number) going to Store A, Store B and Store C for Day 1, and Day 2 using Matrix Algebra Approach. What market share values hold Store A, B and C based on Day 2 analysis

Note: Use the formula X1 = X0 P (for Day 1), X2 = X1 P (for Day 2)

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