document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=866147>Question 866147</A>: <I><SPAN STYLE=\"word-break: break-all;\"> suppose you want to build a rectangular bozo such that its height is double its width.(the depth of the box could be anything.) if you want the surface area to be 108 square feet, and you want the volume to be as large as possible, what should the dimensions of the box be? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #522137 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=522137\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> z = height<BR>\n" );
document.write( "y = depth<BR>\n" );
document.write( "x = width<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=2x ALIGN=MIDDLE  ALT=\"z=2x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2xy%2B2xz%2B2yz=108 ALIGN=MIDDLE  ALT=\"2xy%2B2xz%2B2yz=108\"   DISABLED_style= \"max-width:90%; height:auto;\" >, total surface area.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2xy%2B2x%2A2x%2B2y%2A2x=108 ALIGN=MIDDLE  ALT=\"2xy%2B2x%2A2x%2B2y%2A2x=108\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4xy%2B2x%5E2=108 ALIGN=MIDDLE  ALT=\"4xy%2B2x%5E2=108\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Sensing advantage in having volume formula all in one variable, x, the transformed surface area formula should be solved for y.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4xy=108-2x%5E2 ALIGN=MIDDLE  ALT=\"4xy=108-2x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28108-2x%5E2%29%2F%284x%29 ALIGN=MIDDLE  ALT=\"y=%28108-2x%5E2%29%2F%284x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >----Actual will use this form<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=27%2Fx-%281%2F2%29x ALIGN=MIDDLE  ALT=\"y=27%2Fx-%281%2F2%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" >----But could use either of these forms once x is found.<BR>\n" );
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document.write( "VOLUME, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xyz=x%28%28108-2x%5E2%29%2F%284x%29%292x ALIGN=MIDDLE  ALT=\"xyz=x%28%28108-2x%5E2%29%2F%284x%29%292x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=%28108-2x%5E2%29x%2F2 ALIGN=MIDDLE  ALT=\"v=%28108-2x%5E2%29x%2F2\"   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%28v=%2854-x%5E2%29x%29 ALIGN=MIDDLE  ALT=\"highlight_green%28v=%2854-x%5E2%29x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Treating v as a calculus problem, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=54x-x%5E3 ALIGN=MIDDLE  ALT=\"v=54x-x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d%2F%28dx%29%29v=54-3x%5E2 ALIGN=MIDDLE  ALT=\"%28d%2F%28dx%29%29v=54-3x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Where is this equal 0?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=54-3x%5E2=0 ALIGN=MIDDLE  ALT=\"54-3x%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=54=3x%5E2 ALIGN=MIDDLE  ALT=\"54=3x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18=x%5E2 ALIGN=MIDDLE  ALT=\"18=x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%289%2A2%29 ALIGN=MIDDLE  ALT=\"x=sqrt%289%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=3%2Asqrt%282%29%29 ALIGN=MIDDLE  ALT=\"highlight%28x=3%2Asqrt%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >------Using this value of x, calculate for y and z. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );