document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1181411>Question 1181411</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Choose one of the following (circle your choice); determine the equations and solve the problem below.<BR>\n" );
document.write( "(Remember to define variables, include a diagram or sketch and interpret your answers in relation to the problem).<BR>\n" );
document.write( "A) A farmer is constructing a pig pen and is using his barn wall as one side of the pen. If he has 32 m of fencing and wants to use it all, determine the dimensions that will produce the maximum area of the pen. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #811316 by </B><A HREF=/tutors/aboutme.mpl?userid=Solver92311><B>Solver92311(821)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Solver92311><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=Solver92311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=811316\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=Solver92311&illustration_name=PigPenFence.jpg\">.\r<BR>\n" );
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document.write( "Length of Fence: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 2x\ +\ y\ =\ 32\">\r<BR>\n" );
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document.write( "Length of Pen as a function of width:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y(x)\ =\ 32\ -\ 2x\">\r<BR>\n" );
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document.write( "Area of pen:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large A\ =\ xy\">\r<BR>\n" );
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document.write( "Area of pen as a function of width:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large A(x)\ =\ 32x\ -\ 2x^2\">\r<BR>\n" );
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document.write( "Take the first derivative:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{dA}{dx}\ =\ 32\ -\ 4x\">\r<BR>\n" );
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document.write( "Set the derivative equal to zero to find an extremum:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 32\ -\ 4x\ =\ 0\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ =\ 8\">\r<BR>\n" );
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document.write( "Take the second derivative:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{d^2A}{dx^2}\ =\ -4\">\r<BR>\n" );
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document.write( "Therefore <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{d^2A}{dx^2}\ <\ 0\ \forall\,x\"> in the domain of A, and therefore the one extremum is guaranteed to be a maximum.\r<BR>\n" );
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document.write( "If the maximum area is obtained when <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ =\ 8\">, then calculate <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y(8)\"> to get the other dimension.\r<BR>\n" );
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document.write( "																<BR>\n" );
document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "From <https://www.algebra.com/cgi-bin/upload-illustration.mpl> <BR>\n" );
document.write( "I > Ø<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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