document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1055475>Question 1055475</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular poster needs to have 2700 square centimeters of printed material surrounded by margins. The margins on the left and right edges need to be 4 cm thick, and the margins on the top and bottom edges need to be 3 cm thick. What should the dimensions of the overall poster be in order to minimize the total area? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #670719 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=670719\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 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;\" > = the total area of printed material<BR>\n" );
document.write( "plus margins in cm2<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+ ALIGN=MIDDLE  ALT=\"+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = one of the dimensions of printed material<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+ ALIGN=MIDDLE  ALT=\"+y+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the other dimension of printed material<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+%28+x+%2B+2%2A3+%29%2A%28+y+%2B+2%2A4+%29+ ALIGN=MIDDLE  ALT=\"+A+=+%28+x+%2B+2%2A3+%29%2A%28+y+%2B+2%2A4+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm2<BR>\n" );
document.write( "------------------------------------<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+%28+x+%2B+6+%29%2A%28+y+%2B+8+%29+ ALIGN=MIDDLE  ALT=\"+A+=+%28+x+%2B+6+%29%2A%28+y+%2B+8+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm2<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%2Ay+=+2700+ ALIGN=MIDDLE  ALT=\"+x%2Ay+=+2700+\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm2<BR>\n" );
document.write( "------------------------------------<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+2700%2Fx+ ALIGN=MIDDLE  ALT=\"+y+=+2700%2Fx+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Plug (2) into (1) <BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+%28+x+%2B+6+%29%2A%28+2700%2Fx+%2B+8+%29+ ALIGN=MIDDLE  ALT=\"+A+=+%28+x+%2B+6+%29%2A%28+2700%2Fx+%2B+8+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+2700+%2B+16200%2Fx+%2B+8x+%2B+48+ ALIGN=MIDDLE  ALT=\"+A+=+2700+%2B+16200%2Fx+%2B+8x+%2B+48+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+16200%2Fx+%2B+8x+%2B+2748+ ALIGN=MIDDLE  ALT=\"+A+=+16200%2Fx+%2B+8x+%2B+2748+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------------------------<BR>\n" );
document.write( "Is this a calculus problem? That would be the only<BR>\n" );
document.write( "way I know how to solve this.<BR>\n" );
document.write( "Set the derivative of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+ ALIGN=MIDDLE  ALT=\"+A+\"   DISABLED_style= \"max-width:90%; height:auto;\" > with respect to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+ ALIGN=MIDDLE  ALT=\"+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+ ALIGN=MIDDLE  ALT=\"+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-16200%2Fx%5E2+%2B+8+=+0+ ALIGN=MIDDLE  ALT=\"+-16200%2Fx%5E2+%2B+8+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+16200%2Fx%5E2+=+8+ ALIGN=MIDDLE  ALT=\"+16200%2Fx%5E2+=+8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+=+16200%2F8+ ALIGN=MIDDLE  ALT=\"+x%5E2+=+16200%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+=+2025+ ALIGN=MIDDLE  ALT=\"+x%5E2+=+2025+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+45+ ALIGN=MIDDLE  ALT=\"+x+=+45+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+2700%2Fx+ ALIGN=MIDDLE  ALT=\"+y+=+2700%2Fx+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+2700%2F45+ ALIGN=MIDDLE  ALT=\"+y+=+2700%2F45+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+60+ ALIGN=MIDDLE  ALT=\"+y+=+60+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%2B+6+=+45+%2B+6+ ALIGN=MIDDLE  ALT=\"+x+%2B+6+=+45+%2B+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%2B+6+=+51+ ALIGN=MIDDLE  ALT=\"+x+%2B+6+=+51+\"   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=+y+%2B+8+=+60+%2B+8+ ALIGN=MIDDLE  ALT=\"+y+%2B+8+=+60+%2B+8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+%2B+8+=+68+ ALIGN=MIDDLE  ALT=\"+y+%2B+8+=+68+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------------------<BR>\n" );
document.write( "The dimensions of the overall <BR>\n" );
document.write( "poster to minimize area is 51 x 68<BR>\n" );
document.write( "----------------------------------<BR>\n" );
document.write( "Here's the plot of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%28x%29+ ALIGN=MIDDLE  ALT=\"+A%28x%29+\"   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+400%2C+400%2C+-30%2C+100%2C+-500%2C+5000%2C+16200%2Fx+%2B+8x+%2B+2748+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-30%2C+100%2C+-500%2C+5000%2C+16200%2Fx+%2B+8x+%2B+2748+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This looks OK - <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%28+51+%29+=+51%2A68+ ALIGN=MIDDLE  ALT=\"+A%28+51+%29+=+51%2A68+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%28+51+%29+=+3468+ ALIGN=MIDDLE  ALT=\"+A%28+51+%29+=+3468+\"   DISABLED_style= \"max-width:90%; height:auto;\" > looks like a minimum\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );