document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1161431>Question 1161431</A>: <I><SPAN STYLE=\"word-break: break-all;\">  how many units must be manufactured and sold to obtain this maximum,  R(x)=160x-0.4x^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #784967 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=784967\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
document.write( "\n" );
document.write( "how many units must be manufactured and sold to obtain this maximum, \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%29=160x-0.4x%5E2 ALIGN=MIDDLE  ALT=\"R%28x%29=160x-0.4x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%29=-0.4x%5E2%2B160x ALIGN=MIDDLE  ALT=\"R%28x%29=-0.4x%5E2%2B160x\"   DISABLED_style= \"max-width:90%; height:auto;\" > this is a parabola that opens down and its maximum is at vertex\r<BR>\n" );
document.write( "\n" );
document.write( "so, rewrite equation in vertex form\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%29=-0.4%28x%5E2-400x%29 ALIGN=MIDDLE  ALT=\"R%28x%29=-0.4%28x%5E2-400x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...complete square\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%29=-0.4%28x%5E2-400x%2Bb%5E2%29-%28-0.4%29b%5E2 ALIGN=MIDDLE  ALT=\"R%28x%29=-0.4%28x%5E2-400x%2Bb%5E2%29-%28-0.4%29b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%29=-0.4%28x%5E2-400x%2B200%5E2%29%2B0.4%2A200%5E2 ALIGN=MIDDLE  ALT=\"R%28x%29=-0.4%28x%5E2-400x%2B200%5E2%29%2B0.4%2A200%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%29=-0.4%28x-200%29%5E2%2B0.4%2A40000 ALIGN=MIDDLE  ALT=\"R%28x%29=-0.4%28x-200%29%5E2%2B0.4%2A40000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%29=-+0.4+%28x+-+200%29%5E2%2B16000 ALIGN=MIDDLE  ALT=\"R%28x%29=-+0.4+%28x+-+200%29%5E2%2B16000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=200 ALIGN=MIDDLE  ALT=\"h=200\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=16000 ALIGN=MIDDLE  ALT=\"k=16000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "vertex is at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200 ALIGN=MIDDLE  ALT=\"200\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16000 ALIGN=MIDDLE  ALT=\"16000\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200 ALIGN=MIDDLE  ALT=\"200\"   DISABLED_style= \"max-width:90%; height:auto;\" > units must be manufactured and sold to obtain this maximum of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16000 ALIGN=MIDDLE  ALT=\"16000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );