A small community has two heating services that offer annual service contracts for home heating: Alpine Heating and Badger Furnaces. Currently, 25% of homeowners have service contracts with Alpine, 30% have service contracts with Badger, and the remainder do not have service contracts. Both companies launch aggressive advertising campaigns to attract new customers, with the following effects on service contract purchases for the next several years: each year 35% of homeowners with no current service contract decide to purchase a contract from Alpine and 40% decide to purchase one from Badger. In addition, 10% of the previous customers at each company decide to switch to the other company, and 5% decide they do not want a service contract.
(A) Draw a transition diagram.
(B) Write the transition matrix.
(C) What percentage of homes will have service contracts with Alpine next year? The year after next?
(D) What percentage of homes will have service contracts with Badger next year? The year after next?