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Appendix C Solutions
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, and this information
can be used to help set pricing and other sales strategies. In this problem, we will analyze the
profit found for sales of decorative tiles.
1.
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 = $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.
Let x = the number of tiles sold per month. The following ttable shows points for
the line:
x =
quantity
p = price sold
42
20
52
10
To get the equation for the line, use (pp
0
) = m(xx
0
)
m =
1
10
10
52
42
10
20

=

=


Using (x,p) = (42, 20), line equation is
(p20) = 1(x42)
p =
20 – x + 42
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
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This note was uploaded on 04/24/2011 for the course CJS 230 taught by Professor Sherman during the Spring '11 term at University of Phoenix.
 Spring '11
 sherman

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