document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1155358>Question 1155358</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A farmer has 2400 ft of fencing and wants to fence off a rectangular field that borders a straight river. He does not need a fence along the river (see the figure). What are the dimensions of the field of largest area that he can fence? \r<BR>\n" );
document.write( "\n" );
document.write( "(a) Experiment with the problem by drawing several diagrams illustrating the situation. Calculate the area of each configuration, and use your results to estimate the dimensions of the largest possible field. (Enter your answers as a comma-separated list.) \r<BR>\n" );
document.write( "\n" );
document.write( "(b) Find a function that models the area of the field in terms of one of its sides. \r<BR>\n" );
document.write( "\n" );
document.write( "(c) Use your model to solve the problem, and compare with your answer to part (a). Maximum area occurs at the following values. <BR>\n" );
document.write( "which is looking for<BR>\n" );
document.write( "smaller dimension:<BR>\n" );
document.write( "larger dimension:\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #777933 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=777933\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Draw the figure and if choosing x for side perpendicular to river and y as side opposite the river, then:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2By=2400 ALIGN=MIDDLE  ALT=\"2x%2By=2400\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2400-2x ALIGN=MIDDLE  ALT=\"y=2400-2x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and if A is AREA, then  <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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28A=x%282400-2x%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28A=x%282400-2x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A is a parabola with a maximum vertex point.<BR>\n" );
document.write( "Zeros are x at 0 and at 1200.<BR>\n" );
document.write( "Maximum A occurs for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=600%29 ALIGN=MIDDLE  ALT=\"highlight%28x=600%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Other dimension is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2400-2%2A600=2400-1200=highlight%281200%29 ALIGN=MIDDLE  ALT=\"y=2400-2%2A600=2400-1200=highlight%281200%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Maximum area is  720000 square feet.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );