Question: A machine tool wears over time and may fail. The failure time measured in months has density fT .t / D 2t=900 for 0

A machine tool wears over time and may fail. The failure time measured in months has density fT .t / D 2t=900 for 0 t 30 and 0 otherwise. If the tool fails it must be replaced immediately at a cost of $1,200. If it is replaced prior to failure the cost is only $300. Consider a replacement policy in which the tool is replaces after c months or when it fails. What is the value of c that minimizes cost per unit time.

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