<PRE><B>Question 223772</B>
Assume the profit earned by an artist in any given year is governed by the function 
P(n) = -2n^2 + 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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You have a quadratic with a=-2,b=20,c=-30
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max occors when x=-b/(2a)=-20/(-4)=5 (number to sell to achieve max profit)
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P(5) = -2(5)^2+20(5)-30
P(5) = -50+100-30
p(5) = 20 (maximum profit)
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Cheers,
Stan H.</PRE>