A small producer uses an industrial boiler in its production procedure. A new boiler can be bought for $10,000 As the boiler gets older, its maintenance costs 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:
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Year of Operation Expenses Resale Value Breakdown 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
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a. At what year of operation should the boiler replaced?
b. What is the expected cost per year for the boiler under the optimal replacement strategy?