document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=881296>Question 881296</A>: <I><SPAN STYLE=\"word-break: break-all;\"> my friend has $828 to spend on a fence for her rectangular garden.  She wants to use cedar fencing which costs $14/foot on one side, and cheaper metal fencing which costs $9 foot on the other three sides.  \r<BR>\n" );
document.write( "\n" );
document.write( "What are the dimensions of the garden with the largest area she can enclose.<BR>\n" );
document.write( "length for cedar side<BR>\n" );
document.write( "width for the other side<BR>\n" );
document.write( "What is the largest area that can be enclosed? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #532102 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=532102\">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=+L+ ALIGN=MIDDLE  ALT=\"+L+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = length of the garden in feet<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;\" > = width of the garden in feet<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 garden in ft2<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+14W+%2B+9W+%2B+2%2A9%2AL+=+828+ ALIGN=MIDDLE  ALT=\"+14W+%2B+9W+%2B+2%2A9%2AL+=+828+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+23W+%2B+18L+=+828+ ALIGN=MIDDLE  ALT=\"+23W+%2B+18L+=+828+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------------<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( "from (1):<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+18L+=+828+-+23W+ ALIGN=MIDDLE  ALT=\"+18L+=+828+-+23W+\"   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+=+46+-+%2823%2F18%29%2AW+ ALIGN=MIDDLE  ALT=\"+L+=+46+-+%2823%2F18%29%2AW+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "By substitution:<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+W%2A%28+46+-+%2823%2F18%29%2AW+%29+ ALIGN=MIDDLE  ALT=\"+A+=+W%2A%28+46+-+%2823%2F18%29%2AW+%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+=+46W+-+%2823%2F18%29%2AW%5E2+ ALIGN=MIDDLE  ALT=\"+A+=+46W+-+%2823%2F18%29%2AW%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------------------------------<BR>\n" );
document.write( "I can say then:<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28W%29+=+-%2823%2F18%29%2AW%5E2+%2B+46W+ ALIGN=MIDDLE  ALT=\"+f%28W%29+=+-%2823%2F18%29%2AW%5E2+%2B+46W+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The maximum occurs at:<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=+-b%2F%282a%29+=+-46%2F%28-23%2F9%29+ ALIGN=MIDDLE  ALT=\"+-b%2F%282a%29+=+-46%2F%28-23%2F9%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+=+18+ ALIGN=MIDDLE  ALT=\"+-b%2F%282a%29+=+18+\"   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+=+18+ ALIGN=MIDDLE  ALT=\"+W%5Bmax%5D+=+18+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Plug this back into (1)<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+23%2A18+%2B+18L+=+828+ ALIGN=MIDDLE  ALT=\"+23%2A18+%2B+18L+=+828+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+414+%2B+18L+=+828+ ALIGN=MIDDLE  ALT=\"+414+%2B+18L+=+828+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+18L+=+414+ ALIGN=MIDDLE  ALT=\"+18L+=+414+\"   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+=+23+ ALIGN=MIDDLE  ALT=\"+L+=+23+\"   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%2AL+ ALIGN=MIDDLE  ALT=\"+A+=+W%2AL+\"   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%5Bmax%5D+=+18%2A23+ ALIGN=MIDDLE  ALT=\"+A%5Bmax%5D+=+18%2A23+\"   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%5Bmax%5D+=+414+ ALIGN=MIDDLE  ALT=\"+A%5Bmax%5D+=+414+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "------------------------------<BR>\n" );
document.write( "The cedar side is 18 ft<BR>\n" );
document.write( "The maximum area is 414 ft2<BR>\n" );
document.write( "---------------------------------<BR>\n" );
document.write( "Here's the plot:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-5%2C+50%2C+-40%2C+450%2C+-%2823%2F18%29%2Ax%5E2+%2B+46x+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-5%2C+50%2C+-40%2C+450%2C+-%2823%2F18%29%2Ax%5E2+%2B+46x+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );