Mary's parents read that the value of a car drops 30% the first year, then 20% per year for 3 years, and then 15% per year. Their experience is that repairs average $50 per year during the 3-year warranty and then increase by $225 each year after that. Their interest rate is 9%, and the car they want is $19,000 new.
(a) If they want to minimize their annual costs, what is their optimal policy?
(b) If buying a car costs $500 in time and fees and selling a car costs $250, what is their optimal policy?