Question 429039: I answered questions 1 and 2 but not sure if they are correct...need help with the rest.
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 = $25, they would sell x = 36 tiles each month. If they lower the price to p = $15, then more people would purchase the tile, and they can expect to sell x = 41 tiles in a month’s time.
1.Write two ordered pairs in the form (x, p) that represent the market research. (2 pts)
(25,36) (15,41)
2.Find the equation of the line for the demand equation using the two points in #1. Write your answer in the form p=mx+b.
plug the numbers into the formula for m to find the slope
m=(41-36)/(15-25) or… m=5/(-10) or… m=(-1)/2
So the equation for p=mx+b is… p=-1/2x+b
Solving for b.
(25,36). p=mx+b or 36= -1⁄2× 25+b, or solving for b: b=36-(-1⁄2)(25).b=97⁄2.
(15,41). p=mx+b or 41= (-1)⁄2 × 15+b, or solving for b: b=41-(-1⁄2)(15).b=97⁄2.
The equation of the line that passes through the points
(25,36) and (15,41)
is
p=-1⁄2 x+97⁄2
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.
3. Substitute the results you found from #2 into the equation R=xp to find the revenue equation. Provide your answer in simplified form. (DO NOT REPLACE THE X, only the P is Replaced with your equation from #2.) (2 pts)
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 $400, and the supplier’s cost for a set of tile is $7 each. Let x represent the number of tile sets.
4. If b represents a fixed cost, what value would represent b? (1 pt)
5. If m represents the cost per tile set, what value would represent m? (1 pt)
6. Find the cost equation for the tile. Write your answer in the form C=mx+b. (2 pts)
The profit made from the sale of tiles is found by subtracting the costs from the revenue.
7. Find the Profit Equation (P) by substituting your equations for R (#3) and C (#6) in the equation . Simplify the equation. (3 pts)
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