Project 11
MAC 2233
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?
avg change:

20
dollars per book
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
?
avg change:
35
dollars per book
What is the total cost of producing
35
books?
36
books? What, then, is the extra cost incurred
from producing the
36
th book?
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 Spring '08
 Smith
 Calculus, Derivative

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