Project 10
MAC 2311
In this project, we explore the average and instantaneous rates of change of to
tal cost, total revenue, and total profit with respect to the number
x
of items
produced/sold.
1. Suppose the total cost
C
(
x
) of producing
x
books is
C
(
x
) = 1200+
x
2

20
x
,
represented by $1200 in storage costs,
x
2
dollars for materials and labor, and
a $20 rebate from the government for each book produced.
What is the total cost of producing 0 books? 20 books? What is the average
change in cost per book of producing the first twenty books?
What is the average change in total cost as
x
changes from 25 to 30. What
does this imply about the extra cost incurred by producing each of books
number 26 through 30 ?
What is the total cost of producing 35 books? 36 books?
What, then, is
the extra cost incurred from producing the 36th book?
Calculate the instantaneous rate of change in total cost when
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 Fall '08
 ALL
 Calculus, Derivative, $20, $1200

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