Question 567796: I need help with this I am also looking for a paid tutor anyone intrested?
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 = $30, they would sell x = 62 tiles each month. If they lower the price to p = $20, then more people would purchase the tile, and they can expect to sell x = 72 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).
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 by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! a. Suppose a market research company finds that at a price of p = $30, they would sell x = 62 tiles each month. If they lower the price to p = $20, then more people would purchase the tile, and they can expect to sell x = 72 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).
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Points: (62,30) and (72,20)
slope = (20-30)/(72-62) = -10/10 = -1
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Form: p = mx + b
Solve for "b":
20 = (-1)72 + b
b = 20 + 72 = 92
Equation:
p = -x+92
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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.
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R(x) = x(-x+92) = -x^2+92x
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Cheers,
Stan H.
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