A high-tech company purchases a new computing system whose initial value is V. The system will depreciate at the rate f = f(t) and will accumulate maintenance costs at the rate g = g(t), where t is the time measured in months. The company wants to determine the optimal time to replace the system. (a) Let – { t56) + glo]ds C(t) Show that the critical numbers of C occur at the num- bers t where C(t) =ft) + g(t). (b) Suppose that V V t if 0 30 Vr? and g(t) t>0 12,900 Determine the length of time T for the total deprecia- tion Dt) = f% f(s) ds to equal the initial value V. (c) Determine the absolute minimum of C on (0, T]. (d) Sketch the graphs of C and f + g in the same coordi- nate system, and verify the result in part (a) in this case.
A high-tech company purchases a new computing system whose initial value is V. The system will depreciate at the rate f = f(t) and will accumulate maintenance costs at the rate g = g(t), where t is the time measured in months. The company wants to determine the optimal time to replace the system. (a) Let – { t56) + glo]ds C(t) Show that the critical numbers of C occur at the num- bers t where C(t) =ft) + g(t). (b) Suppose that V V t if 0 30 Vr? and g(t) t>0 12,900 Determine the length of time T for the total deprecia- tion Dt) = f% f(s) ds to equal the initial value V. (c) Determine the absolute minimum of C on (0, T]. (d) Sketch the graphs of C and f + g in the same coordi- nate system, and verify the result in part (a) in this case.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
![A high-tech company purchases a new computing system
whose initial value is V. The system will depreciate at the
rate f = f(t) and will accumulate maintenance costs at
the rate g = g(t), where t is the time measured in months.
The company wants to determine the optimal time to
replace the system.
(a) Let
– { t56) + glo]ds
C(t)
Show that the critical numbers of C occur at the num-
bers t where C(t) =ft) + g(t).
(b) Suppose that
V
V
t if 0<t< 30
450
f(1)
15
if t> 30
Vr?
and
g(t)
t>0
12,900
Determine the length of time T for the total deprecia-
tion Dt) = f% f(s) ds to equal the initial value V.
(c) Determine the absolute minimum of C on (0, T].
(d) Sketch the graphs of C and f + g in the same coordi-
nate system, and verify the result in part (a) in this
case.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F426751df-cc1c-4a4e-8159-36910b8b7824%2F13c206dc-8bff-4542-9589-0854952ba1f0%2Fkyddquj.png&w=3840&q=75)
Transcribed Image Text:A high-tech company purchases a new computing system
whose initial value is V. The system will depreciate at the
rate f = f(t) and will accumulate maintenance costs at
the rate g = g(t), where t is the time measured in months.
The company wants to determine the optimal time to
replace the system.
(a) Let
– { t56) + glo]ds
C(t)
Show that the critical numbers of C occur at the num-
bers t where C(t) =ft) + g(t).
(b) Suppose that
V
V
t if 0<t< 30
450
f(1)
15
if t> 30
Vr?
and
g(t)
t>0
12,900
Determine the length of time T for the total deprecia-
tion Dt) = f% f(s) ds to equal the initial value V.
(c) Determine the absolute minimum of C on (0, T].
(d) Sketch the graphs of C and f + g in the same coordi-
nate system, and verify the result in part (a) in this
case.
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