SOLUTION: Assume the profit earned by an artist in any given year is governed by the function: P(n) = -2n2 + 20n � 30 where n represents the number of paintings sold and P (in thousands of

Question 224400: Assume the profit earned by an artist in any given year is governed by the function: P(n) = -2n2 + 20n � 30 where n represents the number of paintings sold and P (in thousands of dollars) represents the profit. How many paintings should be sold to create a maximum profit? What is the maximum profit?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Assume the profit earned by an artist in any given year is governed by the function: P(n) = -2n2 + 20n � 30 where n represents the number of paintings sold and P (in thousands of dollars) represents the profit. How many paintings should be sold to create a maximum profit? What is the maximum profit?
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P is a quadratic with a = -2 and b = 20 (number of paintings need to be sold)
Maximum P occurs at n = -b/2a = -20/-4 = 5
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P(5) = -2(5)^2 + 20*5 - 30 = -50 + 100 - 30
P(5) = $20 (maximum profit)
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Cheers,
Stan H.
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