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EAurand MAT/117 2/13/11
Axia College Material
Appendix C
Score: x/40
CERTIFICATE OF ORIGINALITY: I certify that this paper, which was produced for the class
identified above, is my original work and has not previously been submitted by me or by anyone
else for any class. I have received no outside help in the preparation of this assignment except
for that provided by my instructor or Axia college. This paper includes no trademarked material,
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agree that submitting this paper shall have the same validity as my handwritten signature.
Polynomials
Retail companies must keep close track of their operations 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 File menu. Click the white space
below each question to maintain proper formatting.
1. In this problem, we 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 a market research company finds that at a price of p = \$20, they would sell x =
42 tiles each month. If they lower the price to p = \$10, then more people would purchase
the tile, and they can expect to sell x = 52 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).
So we have the following two
points: (42,20) and (52,10). Now
we must find the equation of the
line containing this two points.
So:








x-42=20-p p=20+42-x
p=-x+62
A company’s revenue is the amount of money that comes in from sales, before business costs
are subtracted. For a single product, you can find the revenue by multiplying the quantity of the
product sold, x, by the demand equation, p.
b. Substitute the result you found from part a. into the equation R = xp to find the revenue

EAurand MAT/117 2/13/11
In order to find the answer we
simply replace p=-x+62 in the
equation. So:
R=xp R=x(-x+62) R=-
x
2
+62x
The costs of doing business for a company can be found by adding fixed costs, such as rent,
insurance, and wages, and variable costs, which are the costs to purchase the product you are
selling. The portion of the company’s fixed costs allotted to this product is \$300, and the
supplier’s cost for a set of tile is \$6 each. Let x represent the number of tile sets.
c. If b represents a fixed cost, what value would represent b?
b represents the fixed cost, so
from all the data above b=300
d. Find the cost equation for the tile. Write your answer in the form C = mx + b.
As it was shown above, b
represents the fixed cost, so
b=300 whereas m represents the
supplier ‘s cost, so m=6. So
replacing this values we get:
C=6x+300
The profit made from the sale of tiles is found by subtracting the costs from the revenue.
e. Find the Profit Equation by substituting your equations for R and C in the equation
. Simplify the equation.
P=R-C P=-x
2
+62x-(6x+300)
P=-x
2
+62x-6x-300 P=-
x
2
+56x-300
f. What is the profit made from selling 20 tile sets per month?
We simply replace x=20 in the
above equation. So:
P=-20
2
+56×20-300 P=-
400+1120-300 P=420

EAurand MAT/117 2/13/11
g. What is the profit made from selling 25 tile sets each month?
We simply replace x=25 in the
above equation. So:
P=-25
2
+56×25-300 : P=-
625+1400-300 P=475
In order to find out we solve the
equation for x=0. So:
P=-0
2
+56×0-300 P=-300
cost that is paid no matter how
many tiles are sold. In this case if
no tiles are sold there would be
300 dollars lost because of the
fixed cost that must be paid.
i. Use trial and error to find the quantity of tile sets per month that yields the highest profit.
For a quadratic equation we can
use the formula:


in order
to find the amount of tiles that
need to be sold for a maximum
profit:


x=28
This means that 28 sets of tiles
must be sold for maximum profit.
j. How much profit would you earn from the number you found in part i?
In order to find out we
simply replace x=28 in the
equation. So:
P=-28
2
+56×28-300 P=-
784+1568-300 P=484

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