Expert: Paul Klarreich - 12/3/2007

Question
the question is:
given marginal revenue R'(x)= 10 and marginal cost C'(x)= 80-0.1x
Fixed cost are $30, find the profit to be made from producing and selling 100 units of the product.

Answer
Questioner:   Dyan
Category:  Calculus
Private:  No
 
Subject:  Business Calculus
Question:  the question is:
given marginal revenue R'(x)= 10 and marginal cost C'(x)= 80-0.1x
Fixed cost are $30, find the profit to be made from producing and selling 100 units of the product.
-----------------------------------------------
Hi, Dyan,

Please, if you are going to use specialized business jargon, write the definitions of your terms.

I assume that:

marginal revenue R'(x)= 10

means  R(x) = 10x

and that

marginal cost C'(x)= 80-0.1x

means C(x) = 80x - 0.05x^2 + 30

Then I assume that P(x) = profit = R(x) - C(x) =

10x - 80x + 0.05x^2 - 30

so then

P(100) = 10(100) - 80(100) +0.05(100)^2 - 30

= 1000 - 8000 +0.05(10000) - 30

=  - 7000 + 5000 - 30
= -2030