document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=829230>Question 829230</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the minimum dimensions of an open-top rectangular box that is twice as long as it is wide and can hold 12 cubic yards of material. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #499744 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39623)</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=499744\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x=length<BR>\n" );
document.write( "y=width<BR>\n" );
document.write( "z=height\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2y ALIGN=MIDDLE  ALT=\"x=2y\"   DISABLED_style= \"max-width:90%; height:auto;\" >; base area is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy=%282y%29y=2y%5E2 ALIGN=MIDDLE  ALT=\"xy=%282y%29y=2y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >;<BR>\n" );
document.write( "volume, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xyz=12 ALIGN=MIDDLE  ALT=\"xyz=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z2y%5E2=12 ALIGN=MIDDLE  ALT=\"z2y%5E2=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=zy%5E2=6 ALIGN=MIDDLE  ALT=\"zy%5E2=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=%281%2Fy%5E2%296 ALIGN=MIDDLE  ALT=\"z=%281%2Fy%5E2%296\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=6y%5E%28-2%29 ALIGN=MIDDLE  ALT=\"z=6y%5E%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This still has two variables.  Both unknown but one of them depends on the other.  This has no minimum set of dimensions.  Choose any positive z and it determines the needed positive y; or choose any positive y and this determines z.\r<BR>\n" );
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document.write( "Even if you try finding derivative and looking for some extreme point, none is!\r<BR>\n" );
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document.write( "z as a function of y:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-1%2C10%2C-1%2C10%2C6x%5E%28-2%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-1%2C10%2C-1%2C10%2C6x%5E%28-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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