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An auto insurance company classifies its customers in three categories: poor, satisfactory, and preferred. Each year, 25% of those in the poor category are moved to satisfactory and 25% of those in the satisfactory category are moved to preferred. Also, 25% in the preferred category are moved to the satisfactory category, and 25% of those in the satisfactory category are moved to the poor category. Customers are never moved from poor to preferred, or conversely, in a single year. Assuming these percentages remain valid over a long period of time, how many customers can the company expect to have in each category in the long run? Consumers in a certain state can choose between three long-distance telephone services: GTT, NCJ, and Dash. Aggressive marketing by all three companies results in continual shift of customers among the three services. Each year, GTT loses 5% of its customers to NCJ and 15% to Dash, NCJ loses 5% of its customers to GTT and 15% to Dash, and Dash loses 15% of its customers to GTT and 30% to NCJ. Assuming that these percentages remain valid over a long period of time, what is each company's expected market share in the long run? Once a year employees at a company are given the opportunity to join one of three pension plans, A, B, or C. Once an employee decides to join one of these plans, the employee cannot drop the plan or switch to another plan. Past records indicate that each year 14% of the employees elect to join plan A, 16% elect to join plan B, 10% elect to join plan C, and the remainder to not join any plan. (1) In the long run, what percentage of employees will elect to join plans A, B, and C? (2) On average, how many years will it take an employee to decide to join a plan? Two equally competitive pet shops want to locate stores in Lake Tahoe, where there are currently none. There are three main business centers. Tahoe City serves 16% of the population, Incline Village 62% and South Lake Tahoe 22%. If both shops locate in the same center, they split all the business equally; if they locate in different centers, they each get all the business in the center in which they locate plus half the business in the third center. Where should the pet shops locate? Set up a game matrix and solve. You have inherited S 10,000 just prior to a presidential election and you wish to invest it in solar energy and oil stocks. An investment advisor provides you with a payoff matrix that indicates your probable 4-year gains, depending on which party comes into office. What should you invest your money in so that you would have the largest expected gain irrespective of how the election turns out? Player C (fate) Republican Democrat Solar energy [ 3000 2000 Oil 2000 5000 Player R (you)

1 ans) Transition matrix(A) = Calculating A^n we get a steady state value = So in the long run there will be 33% customers in poor, satisfactory and preferred categories. 2) Transition matrix(A) = Calculating A^n we get = GTT company’s expected market share in the long run is 30% and NCJ...

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1 ans) Transition matrix(A) = Calculating A^n we get a steady state value = So in the long run there will be 33% customers in poor, satisfactory and preferred categories. 2) Transition matrix(A) = Calculating A^n we get = GTT company’s expected market share in the long run is 30% and NCJ...