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

Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section: Chapter Questions
Problem 33CT
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A manufacturing company owns a major piece of equip -
ment that depreciates at the (continuous) rate f= f(t) ,
where is the time measured in months since its last overhaul.
Because a fixed cost is incurred each time the
machine is overhauled, the company wants to determine the
optimal time T (in months) between overhauls.
(a) Explain why ∫0t f(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)  =1/t[A  +  ∫0t  f(s) ds]
What does C represent and why would the company
want to minimize C ?
(c) Show that has a minimum value at the numbers t =T
where C(T) =f(T).

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