Algebra Appendic C

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Associate Level Material
Appendix C

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.

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.

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=42,p=20
20=42+b
X=52,p=10
52m+b
M=-1,b=62 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 equation. Provide your answer in simplified form.

520r=52x∙10p=

The costs of doing business for a company can be found by adding fixed…...

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