Mathematics, 07.10.2019 23:30, jeanbeansmith2p2ofty
Custom office makes a line of executive desks. it is estimated that the total cost for making x units of their senior executive model is represented by the following function, where c(x) is measured in dollars/year.
c(x) = 95x + 23
(a) find the average cost function c.
c(x) = 1
(b) find the marginal average cost function c '.
c '(x) =2
(c) what happens to c(x) when x is very large?
lim_(x-> infinity) c(x) = 3
Answers: 2
is a total cost function. Then the average cost function, denoted by 
, is 
of the average cost function, called the marginal average cost function, measures the rate of change of the average cost function with respect to the number of units produced.
![\lim_{x \to \infty} (\bar{C}(x))=\lim_{x \to \infty} (95+\frac{230000}{x})\\\\\lim _{x\to a}\left[f\left(x\right)\pm g\left(x\right)\right]=\lim _{x\to a}f\left(x\right)\pm \lim _{x\to a}g\left(x\right)\\\\=\lim _{x\to \infty \:}\left(95\right)+\lim _{x\to \infty \:}\left(\frac{230000}{x}\right)\\\\\lim _{x\to a}c=c\\\lim _{x\to \infty \:}\left(95\right)=95\\\\\mathrm{Apply\:Infinity\:Property:}\:\lim _{x\to \infty }\left(\frac{c}{x^a}\right)=0\\\lim_{x \to \infty} (\frac{230000}{x} )=0](/tpl/images/0298/4637/98d3e.png)
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