Question

Suppose that the dollar cost of producing x appliances is c(x)=1000+ 90x- 0.2x 2

A. Find the average cost per appliance of producing the first 140 appliances.
B. Find the marginal cost when 140 appliances are produced.
C. Show that the marginal cost when 140 appliances are produced is approximately the cost of producing one more appliance after the first 110 have been made, by calculating the latter cost directly.

Answer 1

Explanation:

Given that the dollar cost of producing x appliances is

`c(x)=1000+ 90x- 0.2x^2`

A) Average cost can be obtained by dividing c(x) by units = x

i.e. average cost =
`(1000)/(x) +90-0.2x`

B) Marginal cost = dC/dx =
`90-0.4x`

When x=140 marginal cost
`= 90-0.4(140)\\=34`

C) We calculate

c(140) =
`=1000+90(140)-0.2(140^2)\\\\=9680`

c(141) =
`=1000+90(141)-0.2(141^2)\\\\\\=9713.80`

Marginal cost = difference = 33.80

Same as 34 shown in marginal cost.