document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=945716>Question 945716</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Maximizing profits: In business, profit is the difference between revenue and cost; that is Total Profit=Total Revenue - Total Cost, P(x)=R(x)-C(x), where x is the number of units sold. Find the maximum profit and the number of units that must be sold in order to yield the maximum profit for <BR>\n" );
document.write( "R(x)=20x-0.1x^2, C(x)=4x+2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #576895 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=576895\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Maximizing profits: In business, profit is the difference between revenue and cost; that is Total Profit=Total Revenue - Total Cost, P(x)=R(x)-C(x), where x is the number of units sold. Find the maximum profit and the number of units that must be sold in order to yield the maximum profit for <BR>\n" );
document.write( "P(x)=20x-0.1x^2, C(x)=4x+2<BR>\n" );
document.write( "P(x)-C(x)=20x-0.1x^2-4x-2=-0.1x^2+16x-2<BR>\n" );
document.write( "P(x)=-0.1(x^2-16x)-2<BR>\n" );
document.write( "complete the square<BR>\n" );
document.write( "P(x)=-0.1(x^2-16x+64)+6.4-2<BR>\n" );
document.write( "P(x)=-0.1(x-8)^2+4.4<BR>\n" );
document.write( "This is an equation of a parabola that opens down with vertex at (8, 4.4)<BR>\n" );
document.write( "maximum profit=4.4 when units sold=8<BR>\n" );
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