Calculus/Calculus

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Question
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 $ _______

Answer
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

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Amos

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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.

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

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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.

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