Math 120 SP08 SBrodnick
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1
1.4
: Linear Models
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1.4: Linear Models
Example
:
1. A cell phone provider charges 15¢ per minute,
plus a $20 monthly fee.
a.
what is the monthly bill if you use 100 minutes?
b.
find monthly cost C if you use x minutes
*
Slope 0.15 is Cost per minute
»
Marginal Cost
is $0.15
Varying quantity is 0.15x
»
Variable Cost
is $0.15x
yintercept is 20
»
Fixed Cost
is $20
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*
Cost Function
: cost C of producing x items
*
Linear Cost Function: C(x) = mx + b
*
Revenue Function
: revenue R of selling x items
*
Linear Revenue Function: R(x) = mx
*
Profit Function
: profit P of producing and
selling x items
*
Profit = Revenue – Cost
P(x) = R(x) – C(x)
1.4: Linear Models
m
arginal cost
fixed cost
m
arginal revenue (price per item)
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Example
:
2.
A tshirt company can make 1000 tshirts
for $1750 and 2000 tshirts for $2560.
a.
Linear
cost function
b.
Fixed
cost?
Marginal
cost?
c.
The company sells each tshirt for $15.
Revenue
function?
d.
Profit
function?
e.
How many tshirts must be sold in order to
break even
?
3.
(#6 P. 78)
1.4: Linear Models
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*
Demand
&
Supply
Functions
*
Demand
Function
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 Spring '08
 Brodnick
 Math, Supply And Demand, $5, $10, $15

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