document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1029100>Question 1029100</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Calculus:\r<BR>\n" );
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document.write( "A fence must be built to enclose a rectangular area of 5000 ft^2. Fencing material costs $1 per foot for the two sides facing north and south and &#8203;$2 per foot for the other two sides. <BR>\n" );
document.write( "Find the cost of the least expensive fence. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #644148 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=644148\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You are asked to minimize expense<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s+ ALIGN=MIDDLE  ALT=\"+s+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the length of one of the sides<BR>\n" );
document.write( "that face north and south and costs $1 / ft<BR>\n" );
document.write( "---------------<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;\" > = area enclosed by fences<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+s%2A%28+5000%2Fs+%29+ ALIGN=MIDDLE  ALT=\"+A+=+s%2A%28+5000%2Fs+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, the sides are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s+ ALIGN=MIDDLE  ALT=\"+s+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5000%2Fs+ ALIGN=MIDDLE  ALT=\"+5000%2Fs+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+ ALIGN=MIDDLE  ALT=\"+P+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the perimeter of the area fenced in<BR>\n" );
document.write( "The perimeter of the area is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+2s+%2B+2%2A%28+5000%2Fs+%29+ ALIGN=MIDDLE  ALT=\"+P+=+2s+%2B+2%2A%28+5000%2Fs+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C+ ALIGN=MIDDLE  ALT=\"+C+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the cost of fencing in the area<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C+=+1%2A%28+2s+%29+%2B+2%2A2%2A%28+5000%2Fs+%29+ ALIGN=MIDDLE  ALT=\"+C+=+1%2A%28+2s+%29+%2B+2%2A2%2A%28+5000%2Fs+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C+=+2s+%2B+20000%2Fs+ ALIGN=MIDDLE  ALT=\"+C+=+2s+%2B+20000%2Fs+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C1+=+2+-+20000+%2F+s%5E2+ ALIGN=MIDDLE  ALT=\"+C1+=+2+-+20000+%2F+s%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Set the 1st derivative, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C1+=+0+ ALIGN=MIDDLE  ALT=\"+C1+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+2+-+20000+%2F+s%5E2+ ALIGN=MIDDLE  ALT=\"+0+=+2+-+20000+%2F+s%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+20000+%2F+s%5E2+=+2+ ALIGN=MIDDLE  ALT=\"+20000+%2F+s%5E2+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s%5E2+=+10000++ ALIGN=MIDDLE  ALT=\"+s%5E2+=+10000++\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s+=+100+ ALIGN=MIDDLE  ALT=\"+s+=+100+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5000%2Fs+=+5000%2F100+ ALIGN=MIDDLE  ALT=\"+5000%2Fs+=+5000%2F100+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5000%2Fs+=+50+ ALIGN=MIDDLE  ALT=\"+5000%2Fs+=+50+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "Plug these results back into original equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C+=+2s+%2B+20000%2Fs+ ALIGN=MIDDLE  ALT=\"+C+=+2s+%2B+20000%2Fs+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C+=+2%2A100+%2B+20000%2F100+ ALIGN=MIDDLE  ALT=\"+C+=+2%2A100+%2B+20000%2F100+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C+=+200+%2B+200+ ALIGN=MIDDLE  ALT=\"+C+=+200+%2B+200+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C+=+400+ ALIGN=MIDDLE  ALT=\"+C+=+400+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The least expensive fence costs $400<BR>\n" );
document.write( "---------------------------------<BR>\n" );
document.write( "check answer:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+s%2A%28+5000%2Fs+%29+ ALIGN=MIDDLE  ALT=\"+A+=+s%2A%28+5000%2Fs+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+100%2A50+ ALIGN=MIDDLE  ALT=\"+A+=+100%2A50+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+5000+ ALIGN=MIDDLE  ALT=\"+A+=+5000+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK -here's the plot of Cost, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C+ ALIGN=MIDDLE  ALT=\"+C+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s+ ALIGN=MIDDLE  ALT=\"+s+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-30%2C+200%2C+-100%2C+600%2C+2x+%2B+20000%2Fx+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-30%2C+200%2C+-100%2C+600%2C+2x+%2B+20000%2Fx+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );