Question 568310: 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 = $6., they would sell x = 44 tiles each month. If they lower the price to p = $2, then more people would purchase the tile, and they can expect to sell x = 48 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), where you are given the values of x and p in the problem. First you need to find the slope of a line using these two points. Then with the slope and one of the points you can find the equation of the line using the point-slope method.( answer- worth 3 points - must show 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. ( answer- worth 3 points - must show 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 $200, and the supplier’s cost for a set of tiles is $5 each. Let x represent the number of tile sets.
c. If b represents a fixed cost, what is the value for b? (answer- worth 3 points):
d. Find the cost equation for the tile. Write your answer in the form C = mx + b.
From part (b) above we know the total cost is the fixed costs plus the variable costs. The variable costs are given as 5$ per tile and the fixed costs is $200. Therefore, the total cost equation is (answer- worth 3 points):
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(revenue) and C(total cost) in the equation . Simplify the equation. (answer- worth 3 points - must show work):
f. What is the profit made from selling 20 tiles per month?(answer- worth 3 points - must show work)
g. What is the profit made from selling 25 tiles each month?(answer- worth 3 points - must show work)
h. What is the profit made from selling no tiles each month? Interpret your answer.(answer- worth 3 points - must show work)
i. Use trial and error to find the quantity of tiles per month that yields the highest profit. (use the profit equation from part e to find the number of tiles that gives the highest profit)(answer- worth 3 points - must show work)
j. How much profit would you earn from the number you found in part i?(answer- worth 3 points - must show work)
k. What price would you sell the tiles at to realize this profit? Hint: Use the demand equation from part a. (answer- worth 3 points - must show 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 1e to solve by setting P = 0, and find your break even values. In other words if you sold x number of tiles then the profit would be zero. You should have two solutions for this problem.(answer- worth 2 points - must show work)
3. In 2006, Apple Computer net sales amounted to $19,315 million. In 2010, its net sales were $65,225 million.
a. Write Apple Computer’s 2006 sales and 2010 sales in scientific notation. (answer- worth 1.5 points - must show work)
You can find the percent of growth in Apple’s sales from 2006 to 2010 by following these steps:
• Find the increase in sales from 2006 to 2010.
• Find what percent that increase is of the 2006 sales.
b. What was the percent growth in Apple’s sales from 2006 to 2010? Do all your work by using scientific notation. (answer- worth 1.5 points - must show work)
Retrieved from http://investor.apple.com/financials.cfm
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 10 feet across and 6 feet tall (see figure). How long should the pieces of PVC plumbing pipe be?
must show work
{the borrom of the trianlge in the figure is 10 feet across and the line in th middle going up is 6 feet need to know the angle}
(answer- worth 2 points)
Concept check problem:(answer- worth 10 points)
5.
a) How do you determine if a polynomial is the difference of two squares?
b) How do you determine if a polynomial is not the difference of two squares?
Write out your explanation using your own words and then give a numeric example for each part (a) and (b) and explain why your example is and is not the difference of two squares. (see page 344 of text the definition).
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! For your demand equation, you have two points (p,x) = (6,44) and (2,48). The slope between these two points is (48-44)/(2-(-6)) = -1. Using point-slope form you have
y-6 = -1(x-44), or
y = -x + 50
Do the rest of the problems using this demand equation.
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