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).
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).
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.CR: Chapter 3 Review
Problem 8CR
Related questions
Question
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).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 6 steps with 6 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Recommended textbooks for you
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning