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Math 71 Supplement 102309
Suppose
x
units of a product is produced in some interval,
$
C x
( )
is the cost of producing
x
units, and
$
R x
( )
is the revenue of producing
x
units. Then the profit
$
P x
( )
is given by
P x
( )
=
R x
( )
"
C x
( )
. The derivatives of these functions
C
'
x
( )
,
R
'
x
( )
,
P
'
x
( )
are called
marginal cost
,
marginal revenue
, and
marginal profit
, respectively. They represent the
rates of changes. However, the practical way to think about these are the following:
C
'
x
( )
"
C x
+
1
( )
#
C x
( )
, the cost of producing one product when
x
units are produced.
R
'
x
( )
"
R x
+
1
( )
#
R x
( )
, the revenue earned from one product when
x
units are produced.
P
'
x
( )
"
P x
+
1
( )
#
P x
( )
, the profit from selling one product when
x
units are produced.
Example:
A company is planning to manufacture and market a microwave oven. After
extensive market analysis, the development and market department provides the
following results: a weekly demand of 200 microwave oven at $160 per unit, and a
weekly demand of 300 microwave oven at $140 per unit. The weekly fixed cost of
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This note was uploaded on 09/08/2010 for the course MATH 71 at San Jose State University .
 '10
 Katsuura,Hidefumi
 Math

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