Suppose a company wants to introduce a new machine that will produce a marginal annual savings in dollars given by S'(x) = 300 -x², where x is the number of years of operation of the machine, while producing marginal annual costs in dollars of C'(x) =x² + 43 -X. 2 a. To maximize its net savings, for how many years should the company use this new machine? b. What are the net savings during the first year of use of the machine? c. What are the net savings over the period determined in part a?
Suppose a company wants to introduce a new machine that will produce a marginal annual savings in dollars given by S'(x) = 300 -x², where x is the number of years of operation of the machine, while producing marginal annual costs in dollars of C'(x) =x² + 43 -X. 2 a. To maximize its net savings, for how many years should the company use this new machine? b. What are the net savings during the first year of use of the machine? c. What are the net savings over the period determined in part a?
Suppose a company wants to introduce a new machine that will produce a marginal annual savings in dollars given by S'(x) = 300 -x², where x is the number of years of operation of the machine, while producing marginal annual costs in dollars of C'(x) =x² + 43 -X. 2 a. To maximize its net savings, for how many years should the company use this new machine? b. What are the net savings during the first year of use of the machine? c. What are the net savings over the period determined in part a?
Transcribed Image Text:Suppose a company wants to introduce a new machine that will produce a
marginal annual savings in dollars given by S'(x) = 300 - x, where x is the number
of years of operation of the machine, while producing marginal annual costs in
43
dollars of C'(x) =x² +
-X.
2
a. To maximize its net savings, for how many years should the company use this
new machine?
b. What are the net savings during the first year of use of the machine?
c. What are the net savings over the period determined in part a?
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
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