document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=171903>Question 171903</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/013600492x/algebrahomeworkh>Algebra & Trigonometry</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> This problem is in the review section about the farmer and fencing.\r<BR>\n" );
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document.write( "A farmer with 10,000 meters of fencing wants to enclose a rectangular field and then divide it into two plots with a fence parallel to one of the sided.  What is the largest area that can be enclosed?\r<BR>\n" );
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document.write( "I really have no clue even where to start by solving this problem, I have searched it and found that we need to maximize the area by using a formula that looks something like(2wx2L=?) but after applying it to my problem I came up with this formula (2Lx3W=10,000.  I have no clue if I am even going in the right direction. I used the two lengths because we have two long sides, and 3 widths because there is also the dividing line of fence that has to be accounted for. Any help is appreciated.\r<BR>\n" );
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document.write( "Thanks,<BR>\n" );
document.write( "Kim </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #127006 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=127006\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This problem is in the review section about the farmer and fencing. <BR>\n" );
document.write( "A farmer with 10,000 meters of fencing wants to enclose a rectangular field and then divide it into two plots with a fence parallel to one of the sides. What is the largest area that can be enclosed? <BR>\n" );
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document.write( "Farmers always want to complicate things, it seems.<BR>\n" );
document.write( "Call W the Width and L the Length with 3 pieces.<BR>\n" );
document.write( "The total length will be 2W + 3L<BR>\n" );
document.write( "The Area is L*W<BR>\n" );
document.write( "so,<BR>\n" );
document.write( "A = L*W<BR>\n" );
document.write( "2W+3L = 10000<BR>\n" );
document.write( "Solve for L<BR>\n" );
document.write( "3L = 10000-2W<BR>\n" );
document.write( "L = (10000-2W)/3<BR>\n" );
document.write( "sub for L into the first eqn<BR>\n" );
document.write( "A = L*W<BR>\n" );
document.write( "A = W*(10000-2W)/3<BR>\n" );
document.write( "A = (10000W - 2W^2)/3<BR>\n" );
document.write( "Now, to find the max, set the 1st derivative = 0.  I don't know if you know what that means, but...<BR>\n" );
document.write( "dA/dW = 10000/3 - 4W/3 = 0<BR>\n" );
document.write( "10000 - 4W = 0<BR>\n" );
document.write( "W = 2500 meters<BR>\n" );
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document.write( "Solve for L<BR>\n" );
document.write( "2W+3L = 10000<BR>\n" );
document.write( "5000 + 3L = 10000<BR>\n" );
document.write( "3L = 5000<BR>\n" );
document.write( "L = 1667 meters<BR>\n" );
document.write( "Area = 2500*5000/3 =~ 4,166,666.67 sq meters<BR>\n" );
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document.write( "Making just a square would have enclosed 5000*5000 = 25,000,000 sq meters, the max area of a rectangle with a given perimeter.<BR>\n" );
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