SOLUTION: The last question that i have is a word problem The relationship between the number (n) of widgets a company sells each week and the price of (p) of each widget is given by the e

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Question 95509: The last question that i have is a word problem
The relationship between the number (n) of widgets a company sells each week and the price of (p) of each widget is given by the equation n=1800-100p and the gross revenue (R) from sales of widgets is calculated by R=np. Determine the maximum possible revenue and the optimum price that will produce that revenue?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The relationship between the number (n) of widgets a company sells each week and the price of (p) of each widget is given by the equation n=1800-100p and the gross revenue (R) from sales of widgets is calculated by R=np. Determine the maximum possible revenue and the optimum price that will produce that revenue?
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Revenue = np
= (1800-100p)p
= 1800p - 100p^2
This is a quadratic with a = -100, b = 1800
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The maximum Revenue occurs at p = -b/(2a)
p = -1800/-200 = 9 (this price will give the maximum Revenue)
maximum revenue will be R(9) = 1800*9-100*9^2
R(9) = 16200-8100 = $8100.00
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Cheers,
Stan H.