7. A small manufacturer uses an industrial boiler in its production process. A new 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 broke-down boiler has no resale value.
Some basic data are given in the following table:
Year of Resale Breakdown
Operation Expenses Value Probability
1 1,500 7,000 0.1
2 2,000 5,000 0.2
3 3,000 4,000 0.4
4 4,500 2,000 0.5
5 6,000 500 0.8
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?
Decision Analysis is guided.