A small manufacturer uses an industrial boiler in its production process.Anew boiler can be purchased for $10,000. As the boiler gets older, its maintenance expenses increase while its resale value declines. Since the boiler will be exposed to heavy use, the probability of a breakdown increases every year. Assume that when a boiler breaks down, it can be used through the end of the year, after which it must be replaced with a new one. Also, assume that a broken-down boiler has no resale value.

Some basic data are given in the following table:

a. At what year of operation should the boiler be replaced?
b. What is the expected cost per year for the boiler, under the optimal replacement strategy?