The Sprott School of Business at Carleton University is trying to determine which of the two copying machines to purchase. Both machines will satisfy the School's needs for the next ten years. Machine 1 costs $2,000 and has a maintenance agreement, which, for an annual fee of $150, covers all repairs. Machine 2 costs $3,000, and its annual maintenance cost is a random variable. At present, the School believes there is a 40% chance that the annual maintenance cost for machine 2 will be $0, a 40% chance it will be $100, and a 20% chance it will be $200. Before the purchase decision is made, the School can have a trained repairer evaluate the quality of machine 2. If the repairer believes that machine 2 is satisfactory, there is 60% chance that its annual maintenance cost will be $0 and a 40% chance it will be $100. If the repairer believes that machine 2 is unsatisfactory, there is 20% chance that the annual maintenance cost will be $0, a 40% chance it will be $100, and a 40% chance it will be $200. There is 50% chance that the repairer will give a satisfactory report. a) Draw the corresponding decision tree and show all your payoffs and the probabilities of each state of nature shown in the decision tree. (10 points) b) Calculate the expected value corresponding at each node shown in the decision tree (show all your work). Please ignore the time value of money. (2 points) c) Determine the School's optimal course of action. (1 point) d) If the repairer charges $40, should the School consider hiring a repairer? Explain your answer by conducting an appropriate analysis. (3 points) MacBook Air