Project 9
MAC 2311
In this project, we explore the average and instantaneous rates of change of total cost, total rev
enue, and total profit with respect to the number
x
of items produced/sold. In particular, note the
interpretations of the calculations, and how they might impact important decisions.
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 govern
ment 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
36
th book?
Calculate the instantaneous rate of change in total cost when
x
= 35
. (Indicate the units for
your answer.) How close is this to the cost you calculated above?
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 Spring '08
 ALL
 Calculus, Derivative

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