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)=212-x2, C'(x)=x2+6/5 x 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?
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)=212-x2, C'(x)=x2+6/5 x 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 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.
Chapter4: Calculating The Derivative
Section4.EA: Extended Application Managing Renewable Resources
Problem 2EA
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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)=212-x2, C'(x)=x2+6/5 x
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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