A manufacturing company owns a major piece of equipment that depreciates at the (continuous) rate f = f (t), where 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 ∫t f(s) ds represents the loss in value of the machine over the period of time since the last overhaul.
(b) Let C = C (t) be given by




What does represent and why would the company want to minimize C?
(c) Show that has a minimum value at the numbers where C (T) = f(T).

Transcribed Image Text:

-[*+Sroa] (s) ds C(1)