document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1166998>Question 1166998</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Horatio, a local farmer and part time magician, wants to create a rectangular compound for his chickens using wire fencing. Furthermore, he needs to divide the compound into two rectangular pens, to separate the roosters from the hens, by installing a dividing fence in the middle. He has 450 meters of fence. Determine the dimensions maximizing the enclosed area. What is the maximum area? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #791558 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=791558\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> he needs to divide the compound into two rectangular pens, to separate the roosters from the hens, by installing a dividing fence in the middle.<BR>\n" );
document.write( " He has 450 meters of fence. <BR>\n" );
document.write( " Determine the dimensions maximizing the enclosed area.<BR>\n" );
document.write( "let L = the length of the compound<BR>\n" );
document.write( "Let w = the width<BR>\n" );
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document.write( "2L + 3w = 450,  w has two sides and the dividing fence<BR>\n" );
document.write( "2L = (450-3w)<BR>\n" );
document.write( "divide by 2<BR>\n" );
document.write( "L = (225-1.5w)<BR>\n" );
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document.write( "A = L * w<BR>\n" );
document.write( "Replace L with (225-1.5w)<BR>\n" );
document.write( "A = w(225-1.5w)<BR>\n" );
document.write( "A = 225w - 1.5w^2<BR>\n" );
document.write( "a quadratic equation<BR>\n" );
document.write( "-1.5w^2 + 225w = 0<BR>\n" );
document.write( "max area occurs on the axis of symmetry, x=-b/(2a), which is<BR>\n" );
document.write( "w = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-225%29%2F%282%2A-1.5%29 ALIGN=MIDDLE  ALT=\"%28-225%29%2F%282%2A-1.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "w = 75 ft is the width of max area<BR>\n" );
document.write( "then<BR>\n" );
document.write( "L = 225 - 1.5(75)<BR>\n" );
document.write( "L = 225 - 112.5<BR>\n" );
document.write( "L = 112.5 ft is the length of max area<BR>\n" );
document.write( ":<BR>\n" );
document.write( " What is the maximum area?<BR>\n" );
document.write( "112.5 * 75 = 8,437.5 sq/ft<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );