document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=224713>Question 224713</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Assume the profit earned by an artist in any given year is governed by the function \r<BR>\n" );
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document.write( "P(n) = -2n2 + 20n – 30\r<BR>\n" );
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document.write( "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 #167840 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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/cgi-bin/show-face.mpl?user=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=167840\">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:<BR>\n" );
document.write( "P(n) = -2n^2 + 20n – 30<BR>\n" );
document.write( "where n represents the number of paintings sold and P (in thousands of dollars) represents the profit. <BR>\n" );
document.write( "How many paintings should be sold to create a maximum profit?<BR>\n" );
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document.write( "This is a quadratic equation; find the axis of symmetry:<BR>\n" );
document.write( "This formula x = -b/(2a)<BR>\n" );
document.write( "In this equation x=n; b=20; a=-2<BR>\n" );
document.write( "n = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-20%29%2F%282%2A-2%29 ALIGN=MIDDLE  ALT=\"%28-20%29%2F%282%2A-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "n = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-20%29%2F%28-4%29 ALIGN=MIDDLE  ALT=\"%28-20%29%2F%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "n = +5 paintings for max profit<BR>\n" );
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document.write( "What is the maximum profit?<BR>\n" );
document.write( "Substitute 5 for n in the original equaiton<BR>\n" );
document.write( "p(n) = -2(5^2) + 20(5) - 30<BR>\n" );
document.write( "p(n) = -2(25) + 100 - 30<BR>\n" );
document.write( "p(n) = -50 + 100 - 30<BR>\n" );
document.write( "p(n) = $20 thousand profit  </SPAN>\n" );
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