View the step-by-step solution to:

# A high-tech company purchases a new computing system whose initial value is V.

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 C(t)=1/t the integral from 0 to t of [f(s)+g(s)]ds.  Show that the critical numbers of C occur at the numbers t where C(t)=f(t)+g(t).
b) Suppose that f(t)=V/15-[V/(450)]t if 0 is less than t and t is less than or equal to 30; f(t)=0 if t is greater than 30; and g(t)=(Vt^2)/12900 if t is greater than 0.  Determine the length of time T for the total depreciation D(t)=the integral from 0 to t of f(s)ds to equal the initial value V.
c) Sketch the graphs of C and f+g in the same coordinate 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 C(t)=1/t the integral from 0 to t of [f(s)+g(s)]ds. Show that the critical numbers of C occur at the numbers t where C(t)=f(t)+g(t).
b) Suppose that f(t)=V/15-[V/(450)]t if 0 is less than t and t is less than or equal to 30; f(t)=0 if t is greater than 30; and g(t)=(Vt^2)/12900 if t is greater than 0. Determine the length of time T for the total depreciation D(t)=the integral from 0 to t of 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 coordinate system, and verify the result in part (a) in this case.

## This question was asked on Feb 08, 2011.

### Why Join Course Hero?

Course Hero has all the homework and study help you need to succeed! We’ve got course-specific notes, study guides, and practice tests along with expert tutors and customizable flashcards—available anywhere, anytime.

### -

Educational Resources
• ### -

Study Documents

Find the best study resources around, tagged to your specific courses. Share your own to gain free Course Hero access or to earn money with our Marketplace.

Browse Documents
• ### -

Question & Answers

Get one-on-one homework help from our expert tutors—available online 24/7. Ask your own questions or browse existing Q&A threads. Satisfaction guaranteed!

Ask a Question
• ### -

Flashcards

Browse existing sets or create your own using our digital flashcard system. A simple yet effective studying tool to help you earn the grade that you want!

Browse Flashcards