A firm has decided to use more energy-efficient equipment that is expected to produce a savings rate (in thousands of dollars per year) of S '(x) = 60–4x , where x is the number of years the equipment has been in place. There will be new costs associated with the equipment that are projected to be at a rate (in thousands of dollars per year) of C'(x) = x² +x+10 . To maximize savings, how long should this firm use the new equipment? What are the net savings (in thousands of dollars) over this period? Please show all integration by hand, though you can use fnInt to check your answer.
A firm has decided to use more energy-efficient equipment that is expected to produce a savings rate (in thousands of dollars per year) of S '(x) = 60–4x , where x is the number of years the equipment has been in place. There will be new costs associated with the equipment that are projected to be at a rate (in thousands of dollars per year) of C'(x) = x² +x+10 . To maximize savings, how long should this firm use the new equipment? What are the net savings (in thousands of dollars) over this period? Please show all integration by hand, though you can use fnInt to check your answer.
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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Transcribed Image Text:A firm has decided to use more energy-efficient equipment that is expected to
produce a savings rate (in thousands of dollars per year) of S '(x) = 60 – 4x , where x is the
number of years the equipment has been in place. There will be new costs associated with the
equipment that are projected to be at a rate (in thousands of dollars per year) of
C'(x) = x² +x+10 . To maximize savings, how long should this firm use the new equipment?
What are the net savings (in thousands of dollars) over this period? Please show all integration
by hand, though you can use fnlnt to check your answer.
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