Please help me out with this problem! I am frustrated with all the decimals that I have to deal with. I don't know if I am doing it correctly.
Suppose that you are setting up a pizza delivery business with three stores, Alpha Pizza in Flushing, Beta Pizza in Long Island City, and Gamma Pizza in Jamaica. When a customer calls a store, that store sends out a delivery person, who delivers the pizza and then returns to the closest store. Because of this, the delivery people end up transitioning from store to store throughout the night. Suppose that when Alpha Pizza is called, then 1/2 of the time the delivery person returns to Alpha, 1/5 of the time the delivery person goes to Beta, and 3/10 of the time goes to Gamma. When Beta Pizza is called, then 3/5 of the time the delivery person returns to Beta and with proababilty 1/5 the person goes to each of Alpha or Gamma. When Gamma Pizza is called, then 3/5 of the time the delivery person returns to Gamma, 4/15 of the time goes to Alpha, and 2/15 of the time goes to Beta. Use a Markov Chain to determine the equilibrium distribution of the delivery people at the end of the day.