document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=988965>Question 988965</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me on this one....A farmer has 60m of fencing to make a rectangular pen for his goat, find the maximum possible area of the pen.... i tried to derive the expression : l=30-w. And the expression for the area in terms of the width : A=-w^2 +30w </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #609433 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=609433\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> length L<BR>\n" );
document.write( "width w<BR>\n" );
document.write( "A for AREA\r<BR>\n" );
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document.write( "perimeter is 60 feet, equal to the amount of fencing.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2w%2B2L=60 ALIGN=MIDDLE  ALT=\"2w%2B2L=60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%2BL=30 ALIGN=MIDDLE  ALT=\"w%2BL=30\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=wL ALIGN=MIDDLE  ALT=\"A=wL\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=w%2830-w%29 ALIGN=MIDDLE  ALT=\"A=w%2830-w%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=30w-w%5E2 ALIGN=MIDDLE  ALT=\"A=30w-w%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=-w%5E2%2B30w ALIGN=MIDDLE  ALT=\"A=-w%5E2%2B30w\"   DISABLED_style= \"max-width:90%; height:auto;\" >------Just as you have.\r<BR>\n" );
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document.write( "Your question is, what is w and L for maximum area A ?\r<BR>\n" );
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document.write( "w and L must be each greater than 0. <BR>\n" );
document.write( "A is a parabola function and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=-w%5E2%2B30w ALIGN=MIDDLE  ALT=\"A=-w%5E2%2B30w\"   DISABLED_style= \"max-width:90%; height:auto;\" >  has a maximum point for its vertex; and A has two x-axis intercepts.  The maximum value for A occurs in the exact middle of the roots.  w is really the HORIZONTAL number line and A is for the vertical number line.  \r<BR>\n" );
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document.write( "Roots for A?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-w%5E2%2B30w=0 ALIGN=MIDDLE  ALT=\"-w%5E2%2B30w=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solve for w, and find what is the value in the middle?<BR>\n" );
document.write( "Now, what is A at that middle value of w? </SPAN>\n" );
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