document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1099767>Question 1099767</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a) A rectangular pen is build with one side against a barn. If 2100 m of fencing are used for the other three sides of the pen, what dimensions maximize the area of the pen?<BR>\n" );
document.write( "b) A rancher plans to make four identical and adjacent rectangular pens against a barn, each with an area of 400m^2. What are the dimensions of each pen that minimize the amount of fence that must be used? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #714236 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=714236\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (a)<BR>\n" );
document.write( "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 length of the <BR>\n" );
document.write( "side perpendicular to the barn<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2100+-+2W+ ALIGN=MIDDLE  ALT=\"+2100+-+2W+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the length of the side<BR>\n" );
document.write( "parallel to the barn<BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+W%2A%28+2100+-+2W+%29+ ALIGN=MIDDLE  ALT=\"+A+=+W%2A%28+2100+-+2W+%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+=+-2W%5E2+%2B+2100W+ ALIGN=MIDDLE  ALT=\"+A+=+-2W%5E2+%2B+2100W+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The formula for the W-value of the<BR>\n" );
document.write( "maximum is:<BR>\n" );
document.write( "<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( "<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+=+2100+ ALIGN=MIDDLE  ALT=\"+b+=+2100+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+W%5Bmax%5D+=+-2100%2F%28+2%2A%28-2%29+%29+ ALIGN=MIDDLE  ALT=\"+W%5Bmax%5D+=+-2100%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=+W%5Bmax%5D+=+525+ ALIGN=MIDDLE  ALT=\"+W%5Bmax%5D+=+525+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2100+-+2W+=+2100+-+2%2A525+ ALIGN=MIDDLE  ALT=\"+2100+-+2W+=+2100+-+2%2A525+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2100+-+1050+=+1050+ ALIGN=MIDDLE  ALT=\"+2100+-+1050+=+1050+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------------------------<BR>\n" );
document.write( "The dimensions that maximize area are:<BR>\n" );
document.write( "525 x 1050 <BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%5Bmax%5D+=+-2%2A%28W%5Bmax%5D%29%5E2+%2B+2100W%5Bmax%5D+ ALIGN=MIDDLE  ALT=\"+A%5Bmax%5D+=+-2%2A%28W%5Bmax%5D%29%5E2+%2B+2100W%5Bmax%5D+\"   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+=+-2%2A525%5E2+%2B+2100%2A525+ ALIGN=MIDDLE  ALT=\"+A%5Bmax%5D+=+-2%2A525%5E2+%2B+2100%2A525+\"   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+=+-551250+%2B+1102500+ ALIGN=MIDDLE  ALT=\"+A%5Bmax%5D+=+-551250+%2B+1102500+\"   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+=+551250+ ALIGN=MIDDLE  ALT=\"+A%5Bmax%5D+=+551250+\"   DISABLED_style= \"max-width:90%; height:auto;\" > m2<BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+525%2A1050+=+551250+ ALIGN=MIDDLE  ALT=\"+525%2A1050+=+551250+\"   DISABLED_style= \"max-width:90%; height:auto;\" > m2<BR>\n" );
document.write( "OK\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );