September 6, 2010, 4:04 am
Polynomials
Polynomials can be used for many different real-world applications. The problems shown below are only some of the possible applications.
Application Practice
Answer the following questions.
1.In this problem, we analyze the profit found for sales of graphic t-shirts. 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 = $25, they would sell x = 60 shirts each month. If they lower the price to p = $15, then more people would purchase the shirts, and they can expect to sell x = 75 shirts 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). Show all your work.
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. Show all your work.
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 $600, and the supplier’s cost for a shirt is $18 each. Let x represent the number of shirts.
c.If b represents a fixed cost, what value would represent b? Show all your work.
d.Find the cost equation for the shirt. Write your answer in the form C = mx + b. Show all your work.
The profit made from the sale of shirts 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. Show all your work.
f.What is the profit made from selling 33 shirts per month? Show all your work.
g.What is the profit made from selling 27 shirts each month? Show all your work.
h.What is the profit made from selling no shirts each month? Interpret your answer. Show all your work.
i.Use trial and error to find the quantity of shirts per month that yields the highest profit. Show all your work.
j.How much profit would you earn from the number you found in part i? Show all your work.
k.What price would you sell the shirts at to realize this profit? Hint: Use the demand equation from part a. Show all your work.
2.The break even values for a profit model are the values for which you earn $0 in profit. Use the equation you created in question one to solve P = 0, and find your break even values. Show all your work.
3.In 2007, Walmart’s sales were reported at $115,140,000,000 as of August of that year. In 2008, its sales were reported at $123,222,000,000.
a.Write Walmart’s 2007 sales and 2008 sales in scientific notation. Show all your work.
You can find the percent of growth in Walmart’s sales from 2007 to 2008 by following these steps:
•Find the increase in sales from 2007 to 2008.
•Find what percent that increase is of the 2007 sales.
b.What was the percent growth in Walmart’s sales from 2007 to 2008? Do all your work by using scientific notation. Show all your work.
Walmart Reports July 2008. (2008). Retrieved from http://walmartstores.com/download/3062.pdf
4.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 30 feet across and 8 feet tall (see figure). How long should the pieces of PVC plumbing pipe be? Show all your work.
