document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=945997>Question 945997</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A farmer wishes to put a fence around a rectangular field and then divide the field into three rectangular plots by placing two fences parallel to one of the sides. If the farmer can afford only 1000 yards of fencing, what dimensions will give the maximum rectangular area? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #577077 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=577077\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+W+ ALIGN=MIDDLE  ALT=\"+W+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the width of the field<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+L+ ALIGN=MIDDLE  ALT=\"+L+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the length of the field<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+ ALIGN=MIDDLE  ALT=\"+A+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the area of the field<BR>\n" );
document.write( "The length of fencing needed is:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4W+%2B+2L+=+1000+ ALIGN=MIDDLE  ALT=\"+4W+%2B+2L+=+1000+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The area is:<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+W%2AL+ ALIGN=MIDDLE  ALT=\"+A+=+W%2AL+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2L+=+1000+-+4W+ ALIGN=MIDDLE  ALT=\"+2L+=+1000+-+4W+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+L=+500+-+2W+ ALIGN=MIDDLE  ALT=\"+L=+500+-+2W+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+W%2A%28+500+-+2W+%29+ ALIGN=MIDDLE  ALT=\"+A+=+W%2A%28+500+-+2W+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+-2W%5E2+%2B+500W+ ALIGN=MIDDLE  ALT=\"+A+=+-2W%5E2+%2B+500W+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The maximum is at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+W%5Bmax%5D+=++-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+W%5Bmax%5D+=++-b%2F%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+-2+ ALIGN=MIDDLE  ALT=\"+a+=+-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+500+ ALIGN=MIDDLE  ALT=\"+b+=+500+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-b%2F%282a%29+=+-500+%2F+%28+2%2A%28-2%29%29+ ALIGN=MIDDLE  ALT=\"+-b%2F%282a%29+=+-500+%2F+%28+2%2A%28-2%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-b%2F%282a%29+=+125+ ALIGN=MIDDLE  ALT=\"+-b%2F%282a%29+=+125+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+L=+500+-+2%2A125+ ALIGN=MIDDLE  ALT=\"+L=+500+-+2%2A125+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+L+=+500+-+250+ ALIGN=MIDDLE  ALT=\"+L+=+500+-+250+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+L+=+250+ ALIGN=MIDDLE  ALT=\"+L+=+250+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "The dimensions for maximum area are:<BR>\n" );
document.write( "250 x 125<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "The length of fencing needed is:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4W+%2B+2L+=+1000+ ALIGN=MIDDLE  ALT=\"+4W+%2B+2L+=+1000+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4%2A125+%2B+2%2A250+=+1000+ ALIGN=MIDDLE  ALT=\"+4%2A125+%2B+2%2A250+=+1000+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+500+%2B+500+=+1000+ ALIGN=MIDDLE  ALT=\"+500+%2B+500+=+1000+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK<BR>\n" );
document.write( "Here's the plot of the area:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-100%2C+300%2C+-4000%2C+35000%2C+-2x%5E2+%2B+500x+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-100%2C+300%2C+-4000%2C+35000%2C+-2x%5E2+%2B+500x+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+250%2A125+=+31250+ ALIGN=MIDDLE  ALT=\"+250%2A125+=+31250+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%5Bmax%5D+=+31250+ ALIGN=MIDDLE  ALT=\"+A%5Bmax%5D+=+31250+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+W+=+125+ ALIGN=MIDDLE  ALT=\"+W+=+125+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "looks OK\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );