Example 5 A business lesson A vendor at a fair knows that she
can sell 300 snow cones per day when the price is
$4
. She can sell 250 when the price is
$4.25
. a) Construct a linear price function. (Let
�
represent the quantity, and
�
,
the price.
)
b
)
Create a revenue function in terms of
�
.

(
Revenue is quantity
×
price.
)
c
)
How many snow cones must she sell, and at what price, in order to maximize revenue?
d
)
What is this maximum revenue?
e
)
Suppose this vendor must pay $
2
0
0
per day for her license to sell snow cones at the fair.
Also suppose her expenses are $
0
.
2
5
per snow cone. Create a cost function in terms of
�
to
express her daily cost of doing business.
f
)
Profit is revenue minus cost. Create her profit function in terms of
�
.
g
)
How many snow cones must she sell, and at what price, in order to maximize profit?
h
)
What is this maximum daily profit?