document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=224400>Question 224400</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #167634 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=167634\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 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?<BR>\n" );
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document.write( "P is a quadratic with a = -2 and b = 20 (number of paintings need to be sold)<BR>\n" );
document.write( "Maximum P occurs at n = -b/2a = -20/-4 = 5<BR>\n" );
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document.write( "P(5) = -2(5)^2 + 20*5 - 30 = -50 + 100 - 30<BR>\n" );
document.write( "P(5) = $20 (maximum profit)<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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