Question 2 Version A Sam has just purchased a new car for $56,500 and it will be traded in for a new one after using 3 years. He has obtained the following estimates of costs for various courses of action: Age of the car (years) 2 3 Resale Value ($) 56,300 56,100 56,000 Operating Cost ($) 1160 1180 1220 (a) Use dynamic programming to find the optimal purchasing policy or strategy which minimizes the total cost over a period of 5 years, and leaves Sam with a new car at the end of this period. Note: For your optimal purchasing policy, you should state both the decision and the cost at the end of each year, and also the total cost over the period of 5 years. [20 marks] (b) If Sam has $12,000 in saving but he can only spend at most 45% of that amount of money. Do you think Sam is able to follow the optimal purchasing policy obtained in (a)? Explain your answer. [3 marks] (c) If Sam doesn't want to replace his car for three consecutive years, which strategy(s) obtained in (a) satisfy this requirement? [2 marks]