A road can be paved with either asphalt or concrete. Concrete costs $15,000/km and lasts 20 years. Assume the annual maintenance costs are $500 for concrete and $800 for asphalt per kilometer per year. Use an interest rate of 8% per year. Contributed by D. P. Loucks, Cornell University
(a) What is the maximum that should be spent for asphalt if it lasts only 10 years?
(b) Assume the asphalt road costs $7000 per kilometer. How long must it last to be the preferred alternative?