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 ofoperation of the machine, while producing a rate of annual costs (in dollars) given by the function C'(x)S'(x) 100-x², C'(x) = x² +14-X.3a. For how many years will it be profitable to use this new machine?The number of profitable years isb. What are the net total savings during the first year of use of the machine?The net total savings during the first year of use of the machine is $(Round to the nearest dollar as needed.)c. What are the net total savings over the entire period of use of the machine?The net total savings over the entire period of use of the machine is $(Round to the nearest dollar as needed.)

Ans. ) Given the question, there is a company that introduces a new machine that produces a rate of…

Answered: Suppose a company wants to introduce a…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section: Chapter Questions

Problem 9T

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. A calculator company found that the cost of producing x graphing calculators per day isC(x) = 4x + e^0.02x.(This ignores the original research and development cost, which is quite large.)(a) If each calculator is priced at $80, find a revenue function, R(x), which gives the revenuefor x calculators sold.(b) Find the profit function, P(x), which gives the profit per day when x calculators areproduced and each later sold for $80.(c) Find the value of x that will maximize P(x). Use the second derivative test to show thatit yields a maximum.(d) Given that one cannot produce a fraction of a calculator, find the daily production levelthat will maximize profit. Please answer in a complete sentence.
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