document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=326076>Question 326076</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A farmer decides to enclose a rectangular garden, using the side of a barn as one side of the rectangle. What is the mazimum area that the farmer can enclose with 100 ft of fence? What should the dementions of the garden be to give this area? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #233486 by </B><A HREF=/tutors/aboutme.mpl?userid=nyc_function><B>nyc_function(2741)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nyc_function><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=nyc_function><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=233486\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> By the way, this is an algebra forum and your question is a calculus question.\r<BR>\n" );
document.write( "\n" );
document.write( "Let P = perimeter of rectangular garden\r<BR>\n" );
document.write( "\n" );
document.write( "P = 100<BR>\n" );
document.write( "2L + 2W = 100<BR>\n" );
document.write( "2(L + W) = 100<BR>\n" );
document.write( "L + W = 100 / 2<BR>\n" );
document.write( "L + W = 50<BR>\n" );
document.write( "W = 50 - L\r<BR>\n" );
document.write( "\n" );
document.write( "Let A = area\r<BR>\n" );
document.write( "\n" );
document.write( "Let W = (50 - L)\r<BR>\n" );
document.write( "\n" );
document.write( "A = LW<BR>\n" );
document.write( "A(L) = L(50 - L)<BR>\n" );
document.write( "A(L) = 50L - L^2\r<BR>\n" );
document.write( "\n" );
document.write( "We now need to find the derivative of A(L).\r<BR>\n" );
document.write( "\n" );
document.write( "A'(L) = 50 - 2L\r<BR>\n" );
document.write( "\n" );
document.write( "For stationary points, set A'(L) = 0\r<BR>\n" );
document.write( "\n" );
document.write( "50 - 2L = 0<BR>\n" );
document.write( "2L = 50<BR>\n" );
document.write( "L = 25\r<BR>\n" );
document.write( "\n" );
document.write( "When L = 24, A'(L) = 50 - 2(24) = 2<BR>\n" );
document.write( "When L = 26, A'(L) = 50 - 2(26) = -2\r<BR>\n" );
document.write( "\n" );
document.write( "Since the graph is increasing, then stationary, then decreasing it is a maximum.\r<BR>\n" );
document.write( "\n" );
document.write( "A(L) = 50L - L^2\r<BR>\n" );
document.write( "\n" );
document.write( "A(25) = 50(25) - 25² \r<BR>\n" );
document.write( "\n" );
document.write( "A(25) = 1250 - 625\r<BR>\n" );
document.write( "\n" );
document.write( "A(25) = 625 square feet\r<BR>\n" );
document.write( "\n" );
document.write( "I hope this helps. <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );