document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=37629>Question 37629</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A farmer has $3600 to spend on fencing for three adjoining rectuangular pastures, all with the same dimensions. a local contracting company tells the farmer that they can build the fence for $6.25/m. What is the largest total area that the farmer can have fenced for that price? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #23236 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=23236\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the fields would look like 3 adjoining rectangles<BR>\n" );
document.write( "with $3600 to spend and and a cost of $6.25/m, the farmer can<BR>\n" );
document.write( "afford 3600/6.25 = 576 m of fence<BR>\n" );
document.write( "He needs 4 north-south lengths and 2 east-west lengths (for example)<BR>\n" );
document.write( "in order to enclose 3 rectangular fields<BR>\n" );
document.write( "All these lengths will add up to 576 m.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+%2B+4y+=+576 ALIGN=MIDDLE  ALT=\"2x+%2B+4y+=+576\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The area enclosed is x times y<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+xy ALIGN=MIDDLE  ALT=\"A+=+xy\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "solve for y in the 1st equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y+=+576+-+2x ALIGN=MIDDLE  ALT=\"4y+=+576+-+2x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+144+-+x%2F2 ALIGN=MIDDLE  ALT=\"y+=+144+-+x%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "substitute this in equation 2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+x%28144+-+x%2F2%29 ALIGN=MIDDLE  ALT=\"A+=+x%28144+-+x%2F2%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+=+-x%5E2%2F2+%2B+144x ALIGN=MIDDLE  ALT=\"A+=+-x%5E2%2F2+%2B+144x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "graph the equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+500%2C+-50%2C+300%2C+-500%2C+12000%2C+-x%5E2%2F2+%2B+144%2Ax%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+500%2C+-50%2C+300%2C+-500%2C+12000%2C+-x%5E2%2F2+%2B+144%2Ax%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I'll guess the x value where the graph is a max is 144<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+-x%5E2%2F2+%2B+144x ALIGN=MIDDLE  ALT=\"A+=+-x%5E2%2F2+%2B+144x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+-%28144%29%5E2%2F2+%2B+144%2A%28144%29 ALIGN=MIDDLE  ALT=\"A+=+-%28144%29%5E2%2F2+%2B+144%2A%28144%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "factor out 144^2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+144%5E2%2A%281+-+1%2F2%29 ALIGN=MIDDLE  ALT=\"A+=+144%5E2%2A%281+-+1%2F2%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+=+144%5E2+%2F+2 ALIGN=MIDDLE  ALT=\"A+=+144%5E2+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+20736%2F2 ALIGN=MIDDLE  ALT=\"A+=+20736%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+10368 ALIGN=MIDDLE  ALT=\"A+=+10368\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The way to test this is to increase 144 a little, test it in the equation<BR>\n" );
document.write( "then decrease 144 a little and test it in the equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+-%28143%29%5E2%2F2+%2B+144%2A%28143%29 ALIGN=MIDDLE  ALT=\"A+=+-%28143%29%5E2%2F2+%2B+144%2A%28143%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+=+10367.5 ALIGN=MIDDLE  ALT=\"A+=+10367.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+-%28145%29%5E2%2F2+%2B+144%2A%28145%29 ALIGN=MIDDLE  ALT=\"A+=+-%28145%29%5E2%2F2+%2B+144%2A%28145%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+=+10367.5 ALIGN=MIDDLE  ALT=\"A+=+10367.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "since the area is a little bit less than 10368 on either side<BR>\n" );
document.write( "of x = 144, then this is the max.<BR>\n" );
document.write( "The largest Area that can be enclosed is 10368<BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "check<BR>\n" );
document.write( "If x = 144, find y<BR>\n" );
document.write( "xy = 10368<BR>\n" );
document.write( "y = 10368/144<BR>\n" );
document.write( "y = 72<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+%2B+4y+=+576 ALIGN=MIDDLE  ALT=\"2x+%2B+4y+=+576\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A144+%2B+4%2A72+=+576 ALIGN=MIDDLE  ALT=\"2%2A144+%2B+4%2A72+=+576\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=288+%2B+288+=+576 ALIGN=MIDDLE  ALT=\"288+%2B+288+=+576\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=576+=+576 ALIGN=MIDDLE  ALT=\"576+=+576\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );