A rural subdivision has several miles of access roads that need a new surface treatment. Alternative 1 is a gravel base and pavement with an initial cost of $500,000 that will last for 15 years and has an annual upkeep cost of $100 per mile. Alternative 2 is to enhance the gravel base now at a cost of $50,000 and immediately coat the surface with a durable hot oil mix, which costs $130 per barrel applied. Annual reapplication of the mix is required. A barrel covers 0.05 mile.

(a) If the discount rate is 6% per year, determine the number of miles at which the two alternatives break even.

(b) A drive in a pickup indicates a total of 12.5 miles of road. Which is the more economical alternative?