document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1106230>Question 1106230</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Find the maximum product of two numbers whose sum is 60. Is there a minimum product? Explain.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #721172 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=721172\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2BB=60 ALIGN=MIDDLE  ALT=\"A%2BB=60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then what is the maximum of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Z=AB ALIGN=MIDDLE  ALT=\"Z=AB\"   DISABLED_style= \"max-width:90%; height:auto;\" >?<BR>\n" );
document.write( "You can substitute from above,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=60-B ALIGN=MIDDLE  ALT=\"A=60-B\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Z=%2860-B%29B ALIGN=MIDDLE  ALT=\"Z=%2860-B%29B\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Z=60B-B%5E2 ALIGN=MIDDLE  ALT=\"Z=60B-B%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So find the maximum of Z.<BR>\n" );
document.write( "Since there is a negative coefficient in front of the quadratic term, the parabola opens downward and has a maximum.<BR>\n" );
document.write( "Since it's a parabola you can convert to vertex form and find the maximum and the location of the maximum. <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );