   Chapter 3.9, Problem 65E

Chapter
Section
Textbook Problem

# A company estimates that the marginal cost (in dollars per item) of producing x items is 1.92 − 0.002 x . If the cost of producing one item is $562, find the cost of producing 100 items. To determine To find: The cost of producing 100 items. Explanation 1) Concept: If F is an antiderivative of f on an interval I, then the most general antiderivative of f on I is Fx+c, where c is an arbitrary constant. 2) Given: The marginal cost of producing x items is 1.92-0.002x and the cost of producing one item is$562.

3) Calculations:

Here, marginal cost is

C'x=1.92-0.002x.

Taking the general antiderivative,

Cx=1.92x-0.002x22+K,  where K as a constant.

It is given that, the cost of producing one item is \$562.

This means C1=562.

So, substitute x=1 in Cx,

C(1)=1.921-0.002122+K

562=1.92-0.001+K

562=1

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