Operations Research Question

Question 4 (30 Points) Suppose that the number of accidents you make in a year is a random variable that follows Poisson distribution with mean 0.5. In each year, you renew your insurance where the insurance company charges you depending on your accident history. The company classifies its customers in 4 categories S={1,2,3,4). Category 1 represents the minimum payment category, where category 4 represents the highest payment. The categories of the customers are adjusted based on their last category and the number of accidents they made in the last year. The adjustments in the categories are given in the table below (e.g. if you are in category 1 and made 2 accidents in this year, you will be in category 3 in the next year). Next category if: No accidents 1 accident 2 accidents 2 3 3 or more accidents 1 1 4 3 4 1 4 Current 2 Category 3 2 4 4 4 4 3 4 4 4 Your yearly payments are $100, $150, $350, 5700 for categories 1,2,3,4 respectively. a) Assume that the company made you an offer saying that your payments may not be based on the categories that are defined above. If you accept their new offer, you will be paying $300 regardless of the number accidents you make. Determine whether you should accept the offer or stay in the previous plan. b) Assume that you rejected the offer in part a. Given that you were in category 4 this year, how long does it take to reach category 1 on average