Question 149747: a.)Suppose that a market research company finds that at a price of p=$20, they would sell x=42 tiles each month. If they lower the price to p=$10, then more people would purchase the tile, and they can expect to sell x=52 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. (write an equation using two points).
b.)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. Substitute the result from part a into the equation R=xp to find the revenue equation.
here is what I have so far:
a.)
my equation are in the form p=mx+b
20 = 42x + b 10 = 52x + b
I think I am supposed to find the difference.
20 = 42x + b
-(10 = 52x + b)
=10 = -52x
This is where I am completely lost. Please help me.
Thanks a lot!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! a.)Suppose that a market research company finds that at a price of p=$20, they would sell x=42 tiles each month. If they lower the price to p=$10, then more people would purchase the tile, and they can expect to sell x=52 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. (write an equation using two points).
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Points: ($20,42) and ($10,52)
slope = (52-42)/(10-20) = -1
Find the intercept:
42 = -1(20) + b
b = 62
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EQUATION:
p = -x + 62
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b.)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. Substitute the result from part a into the equation R=xp to find the revenue equation.
R(x) = x(-x+62) = -x^2+62x
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Cheers,
Stan H.
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