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Axia College Material – MAT 117
Polynomials
Retail companies need to keep close track of their operations in order to maintain profitability. Often, the
sales data of each individual product is analyzed separately, which can be used to help set pricing and
other sales strategies.
Application Practice
Answer the following questions. Use Equation Editor to write mathematical expressions and equations.
First, save this file to your hard drive by selecting
Save As
from the
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menu. Click the white space
below each question to maintain proper formatting.
1. In this problem, we will analyze the profit found for sales of decorative tiles. A
demand equation
(sometimes called a demand curve) shows how much money people would pay for a product
depending on how much of that product is available on the open market. Often, the demand
equation is found empirically (through experiment, or market research).
a. Suppose that a market research company finds that at a price of
p = $60
, they would sell
x =
28
tiles each month. If they lower the price to
p = $40
, then more people would purchase the
tile, and they can expect to sell
x = 38
tiles in a month’s time. Find the equation of the line for
the demand equation. Write your answer in the form p = mx + b. (Hint: Write an equation
using two points in the form (x,p)).
The line of the demand passes through the points (28,60) and (38,40) in the form of (x,p).
Using these points, we can construct the demand equation. To do so, we first need to find
the slope.
=


Slopem y2 y1x2 x1
Or in this situation:
=


Slopemof the demand line p2 p1x2 x1
Using the two points, the slope of the demand line is:
,
=
,
x1 p1 28 60
,
=(
,
)
x2 p2
38 40
=


Slope mof the demand line p2 p1x2 x1
=


40 6038 28
=
2010
MAT 117
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2
We can find the line now using the slopeintercept method since we know the slope,
and 2 points on the line.
We can use either point, but I will choose to use (28,60)
=
+
y mx b
Or in this situation:
=
+
p mx b
=
m
2
=
b unknown
=
x 28
=
p 60
=
+
p mx b
=
+
60
228 b
=
+
60
56 b
=
b 116
Thus the demand equation is:
=
+
p mx b
=
+
=

p
2x 116 or p 116 2x
A company’s
revenue
is the amount of money that comes in from sales, before business costs
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 Spring '09
 mcmillian
 Math, Polynomials

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