There are three types of grocery stores in Surabaya. Within this community (with a fixed population) there always exists a shift of customers from one grocery store to another. On January 1, % shopped at Store 1, 1/3 at Store II and 5/12 at Store III. Each month Store I retains 90% of its customers and losses 10% of them to Store II. Store Il retains 5% of its customers and losses 85% of them to Store and losses 10% of them to Store III. Store Ill retains 40% of its customers and losses 50% of them to Store I and losses 10% of them to Store II. a) Find the transition matrix b) What proportion of customers will each store retain by Feb 1 and March 1? c) Assuming the same pattern continues, what will be the long-run distribution of customers among the three stores?