Question

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) = 158 - x^2 and the rate of annual costs (in dollars) given by the function C'(x) = x^2 + 15/4x, where x is the number of years of operation of the machine. a. For how many years will it take to be profitable to use this new machine? b. What are the net savings of 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) = 158 - x^2 and the rate of annual costs (in dollars) given by the function C'(x) = x^2 + 15/4x, where x is the number of years of operation of the machine.

a. For how many years will it take to be profitable to use this new machine?
b. What are the net savings of 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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Added by Danielle W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

12/03/2022

Step 1

Step 1: Set the rate of annual savings equal to the rate of annual costs to find the intersection point: \[x^2 + \frac{15}{4}x = 158 - x^2\] Show more…

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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) = 158 - x^2 and the rate of annual costs (in dollars) given by the function C'(x) = x^2 + 15/4x, where x is the number of years of operation of the machine. a. For how many years will it take to be profitable to use this new machine? b. What are the net savings of 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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