Suppose a company wants to introduce a new machine that will produce a rate of annual savings​ (in dollars) given by the function S′(x)​, where x is the number of years of operation of the​ machine, while producing a rate of annual costs​ (in dollars) given by the function C′(x)   S′(x)=150−x^2​, C′(x)=x^2+11/4x. a.  For how many years will it be profitable to use this new​ machine? b. What are the net total savings during the first year of use of the​ machine? c. What are the net total savings over the entire period of use of the​ machine?

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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Suppose a company wants to introduce a new machine that will produce a rate of annual savings​ (in dollars) given by the function
S′(x)​,
where x is the number of years of operation of the​ machine, while producing a rate of annual costs​ (in dollars) given by the function C′(x)
 
S′(x)=150−x^2​,
C′(x)=x^2+11/4x.
a.  For how many years will it be profitable to use this new​ machine?
b. What are the net total savings during the first year of use of the​ machine?
c. What are the net total savings over the entire period of use of the​ machine?
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