Operations Research 2

3. Automobile Replacement. Suppose you would like to minimize your automobile transportation costs over the next five years. Let us assume that presently you do not own a car and that over the next four years you will consider buying new cars only at the start of each year. The average price of a new car over the next four years is expected to be $5,000. You decide that you would not keep a car longer than three years. The table below gives the operating costs and trade-in values for each type of car. There is no requirement that you dispose of your car at the end of the fifth year. Your objective is to minimize purchase plus operating costs during years 1-5. Use DP to determine the optimal policy. Age of car Operating costs Brand New $600 (during year 1) 1 year 900 (during year2) 2 years 1200 (during year 3) 3 years Trade-in value at beginning of year $4000 (start of year2) 3,000 (start of year 3) 2,200 (start of year 4)