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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 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
What does 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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