SOLUTION: Suppose that a corporation that manufactors widgets determines that its revenue is R(x)=1000x-x^2 and its cost function is C(x)=3000+20x, where x represents the number of widgets p

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Question 202160: Suppose that a corporation that manufactors widgets determines that its revenue is R(x)=1000x-x^2 and its cost function is C(x)=3000+20x, where x represents the number of widgets produced. Find the corporations maximum profit.
Answer by stanbon(75887) About Me  (Show Source):
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Suppose that a corporation that manufactors widgets determines that its revenue is R(x)=1000x-x^2 and its cost function is C(x)=3000+20x, where x represents the number of widgets produced. Find the corporations maximum profit.
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Profit = Revenue - Cost
Profit = (1000x-x^2)-(3000+20x)
Profit = -x^2 + 980x -3000
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Max Profit occurs when x = -b/2a
x = -980/-2 = 490
Profit is maximized when # of widgets produced is 490.
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Find the corporations maximum profit.
P(490) = -(490)^2 + 980(490) -3000 = $237,100
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Cheers,
Stan H.