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 + 230000
(a) Find the average cost function C.(b) Find the marginal average cost function C.(c) What happens to C(x) when x is very large?

Respuesta :

Answer:

Average cost function is [tex]95+\frac{230000}{x}[/tex]

the marginal average cost function [tex]\frac{230000}{x^2}[/tex]

C(x) approaches infinity when x is very large

Step-by-step explanation:

the total cost for making x units of their Senior Executive model is represented by the following function

[tex]C(x) = 95x + 230000[/tex]

Average cost is C(x) divide by x

Average cost =[tex]\frac{C(x)}{x} =\frac{95x + 230000}{x}[/tex]

Average cost function is [tex]95+\frac{230000}{x}[/tex]

To find marginal average cost function , we take derivative

Derivative of average cost function is

the marginal average cost function  [tex]\frac{230000}{x^2}[/tex]

x is very large means x tends to infinity

Find out the value of C(x) when x approaches infinity

[tex]C(x) = 95x + 230000[/tex]

Plug in infinity for x, c(x) approaches infinity

C(x) approaches infinity when x is very large