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 File 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).

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 months 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)).

Substitute the result you found from part a into the equation R = xp to find the revenue equation. Provide your answer in simplified form.

If b represents a fixed cost, what value would represent b?

Find the cost equation for the tile. Write your answer in the form C = mx + b.

Find the Profit Equation by substituting your equations for R and C in the equation . Simplify the equation.

What is the profit made from selling 15 tile sets per month?

What is the profit made from selling 30 tile sets each month?

What is the profit made from selling no tile sets each month? Interpret your answer.

Use trial and error to find the quantity of tile sets per month that yields the highest profit.

How much profit would you earn from the number you found in part i?

What price would you sell the tile sets at to realize this profit (hint, use the demand equation from part a)?

Suppose Home Depots sales in 2002 were amounted to $59,200,000,000. In 2006, suppose its sales were $109,700,000,000.

Write Home Depots 2002 sales and 2006 sales in scientific notation.

What was the percent growth in Home Depots sales from 2002 to 2006? Do all your work by using scientific notation.

Find the increase in sales from 2002 to 2006.

Find what percent that increase is of the 2002 sales.

(source: Home Depot Annual Report for FY 2006: http://www6.homedepot.com/annualreport/index.html)

A customer wants to make a teepee in his backyard for his children. He plans to use lengths of PVC plumbing pipe for the supports on the teepee, and he wants the teepee to be 24 feet across and 5 feet tall (see figure). How long should the pieces of PVC plumbing pipe be?