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.