Problem 77E

A manufacturing company owns a major piece of equipment that depreciates at the continuous rate f=f(t), where t is the time measured in months since its last overhaul. Because a fixed cost A is incurred each time the machine is overhauled, the company wants to determine the optimal time T in months between overhauls. a Explain why 0tf(s)ds represents the loss in value of the machine over the period of time t since the last overhaul. b Let C=C(t) be given by C(t)=1t[A+0tf(s)ds] What does C represent and why would the company want to minimize C? c Show that C has a minimum value at the numbers t=T where C(T)=f(T).

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