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The total cost (in dollars) of producing x food processors is C(x) = 1500+90x-0.4^2

A Find the exact cost of producing the 31st food processor is $ ____

B Using the marginal cost the approximate cost of producing the 31st food processor is $ _______

Firstly, I am going to assume that you made a typo in your C(x). It should be

C(x) = 1500+90x-0.4 * x^ 2

A. The exact cost of producing the 31 food processor (in dollars) is given by

C(31) = 1500 + 90(31) - 0.4 (31)(31) = ...

(and you can easily find this (and the next) using your calculator.

The exact cost of producing the 30 food processor (in dollars) is given by

C(30) = 1500 + 90(30) - 0.4 (30)(30) = ...

For Exact solution of producing the 31st processor, use C(31) - C(30). Woala!

=

B. The marginal cost (as a function is given by (its derivative)

C'(x) = 0 + 90 (1) - 0.4 * 2 *x

= 90 - 0.8 x

To approximate the cost to produce the 31st food processor, use the theory of differential

Delta C = dC = C'(31) * dx

= ( 90 - 0.8 (30) ) * (1) = 66

So the cost of producing the 31st processor is approximately $66.

The two answers in (A) and (B) should be very close. And that is why we use Calculus to do this kind of problem.

Good luck!

Calculus

Answers by Expert:

I can answer all calculus question. I am a Math Lecturer and I teach Math in a College, usually Calculus 1, Calculus 2 and Calculus 3 and Linear Algebra.

I have been teaching in this college for more than 12 years. Prior to that, I taught for three years as Visiting Assistant Professor.**Education/Credentials**

I got my doctorate from Univ. of Rochester in Algebraic Toppology. I got a MA from Univ of Rochester, an MA from York Univ. in Toronto and almost did my M.Sc in the National Univ. of Singapore.