Class Meeting #3
Apnlications to Business
-The
C,ost function
-Let
C(x) represent
the
total
cost
of
producing
x items
-C(x)=
fixed costs
(non-production
costs)
+
variable costs
(depends
on
#
of
items)
*For
a
linear
model,
C(x)
:
mx
*
b,
where
m
=
cost
to
produce
each item,
b:fixed
costs
-m
is
called the Marginal
Cost.
Example:
The
fixed
costs
of
producing
items
is
$3,200.
The
variable
cost
per
unit is
$25.
Fhd
the equation
for
Total Cost,
C(x)....Do
-The
Revenug function
-If
each
item
or unit sells for
p
(price),
then the
revenue
from
selling
x
units
is
R(x):px
Example: Find
the
revenue
collected
from
selling
x
units
of a
product,
if
each unit
sells for
S55. Do
-The
Profit fifnctiort
-Profit
-
Revenue
-
Total
cost
-Usually
written as r(x)
-Jn
lhe
example
directly
above,
r(x):55x-(25x+3200):55x-25x-3200
:30x-3200
-The
break-even
ooint
is
the
number
of
units
(x)
for which
the
proflt
:0
[R(x)=C(x)]
-Do
for
the
above
example:
*Marginal
Cost,
Marginal revenue,
and Marginal
profit
are the rates
of change
of
these
quantities
per
unit change in
x. Graphically,
these
are
the Slopes of
these
linear
functions
