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Question 414315: Hello,
I have a word problem that requires 4 answers and wondered if you could help. This is the question: ACME Skateboards Inc., has paid consultants to look over last year's sales and provide them with supply and demand equations that fit their sales data. The consultants provided the equation S=0.09x^2-0.45x+3.5 for the company's supply curve where x is the price per skateboard in dollars, and s is the number of skateboards produced in thousands. The consultants also provided D=15-0.5x as the demand curve where x represents the price per skateboard in dollars, and D represents the demand for their product in thousands.
1. What should the price of a skateboard be for the company to break even (round to the nearest penny)
2. What is the demand for ACME's skateboards if the price of a skateboard is $11.14 (round to the nearest hundred)
3. By how many skateboards will demand exceed supply if the price is set at $7.02 per skateboard (round to the nearest hundred).
4. At what price will supply exceed demand by one thousand skateboards? (round to the nearest penny)
Thank you very much for any help with this. I have no idea where to even start.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! ACME Skateboards Inc., has paid consultants to look over last year's sales and provide them with supply and demand equations that fit their sales data. The consultants provided the equation S=0.09x^2-0.45x+3.5 for the company's supply curve where x is the price per skateboard in dollars, and s is the number of skateboards produced in thousands. The consultants also provided D=15-0.5x as the demand curve where x represents the price per skateboard in dollars, and D represents the demand for their product in thousands.
1. What should the price of a skateboard be for the company to break even (round to the nearest penny)
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Solve S(x) = D(x)
0.09x^2-0.45x+3.5 = 15-0.5x
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0.09x^2 + 0.05x - 11.5 = 0
Use the Quadratic formula to get:
x = $11.03
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2. What is the demand for ACME's skateboards if the price of a skateboard is $11.14 (round to the nearest hundred)
D(x) = 15-0.5x
D(11.14) = 15-0.5*11.14
D(11.14) = 9.43
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3. By how many skateboards will demand exceed supply if the price is set at $7.02 per skateboard (round to the nearest hundred).
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Find S(7.02) = 4.78
D(7.02) = 11.49
D(7.02)-S(7.02) = 6.71
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4. At what price will supply exceed demand by one thousand skateboards? (round to the nearest penny)
Solve S(x)-D(x)= 1000
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Cheers,
Stan H.
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