document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=48689>Question 48689</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Maximizing profit.  The total profit (in dollars) for sales of x rowing machines is given by p(x)= -0.2x^2+300x-200 .  What is the profit if 500 are sold?  For what value of x will the profit be at a maximum? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #32223 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=32223\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the differential gives you a turning point on a curve, either a max or a min (or a point of inflexion).\r<BR>\n" );
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document.write( "p(x)= -0.2x^2+300x-200 <BR>\n" );
document.write( "p'(x)= -0.4x+300 where p'(x) is the differential<BR>\n" );
document.write( "p'(x)= -0.4x+300 = 0<BR>\n" );
document.write( "0.4x = 300<BR>\n" );
document.write( "x = 300/0.4<BR>\n" );
document.write( "x = 750\r<BR>\n" );
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document.write( "p''(x) = -0.4 which is NEGATIVE. This is therefore a MAXIMUM point.\r<BR>\n" );
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document.write( "So profit is maximised at x=750\r<BR>\n" );
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document.write( "jon.<BR>\n" );
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