document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1010811>Question 1010811</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If a company makes a block of cheese designed to have the height exactly five times the width and the ideal of 1800mm^3 using the least possible surface area, what would be the length </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #626273 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39630)</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=626273\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Most of the way through, but short of complete finish:\r<BR>\n" );
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document.write( "y, height<BR>\n" );
document.write( "x, length<BR>\n" );
document.write( "z, width\r<BR>\n" );
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document.write( "The description gives from these chosen variables,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=5z%2Cxyz=1800%29 ALIGN=MIDDLE  ALT=\"system%28y=5z%2Cxyz=1800%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and the area function you want, depending on name you choose, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=2xy%2B2yz%2B2xz ALIGN=MIDDLE  ALT=\"A=2xy%2B2yz%2B2xz\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Substitutions to put A as a function of just one single variable...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%285z%29z=1800 ALIGN=MIDDLE  ALT=\"x%285z%29z=1800\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5xz%5E2=1800 ALIGN=MIDDLE  ALT=\"5xz%5E2=1800\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "but z is width, and the question asks for LENGTH to minimize area.<BR>\n" );
document.write( "Try again...<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=y%2F5 ALIGN=MIDDLE  ALT=\"z=y%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use in the volume,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy%28y%2F5%29=1800 ALIGN=MIDDLE  ALT=\"xy%28y%2F5%29=1800\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "still giving a square for what we want to substitute.<BR>\n" );
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document.write( "Try first aiming for one of the other variables for the single variable in A.<BR>\n" );
document.write( "Go back to description, and substitute for y in A.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=2x%285z%29%2B2%2A5zz%2B2xz ALIGN=MIDDLE  ALT=\"A=2x%285z%29%2B2%2A5zz%2B2xz\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=10xz%2B10z%5E2%2B2xz ALIGN=MIDDLE  ALT=\"A=10xz%2B10z%5E2%2B2xz\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=12xz%2Bz%5E2 ALIGN=MIDDLE  ALT=\"A=12xz%2Bz%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >-------want to eliminate, subst for x or z...\r<BR>\n" );
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document.write( "Look again at description.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%285z%29z=1800 ALIGN=MIDDLE  ALT=\"x%285z%29z=1800\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5xz%5E2=1800 ALIGN=MIDDLE  ALT=\"5xz%5E2=1800\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1800%2F%285z%5E2%29=360%2Fz%5E2 ALIGN=MIDDLE  ALT=\"x=1800%2F%285z%5E2%29=360%2Fz%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >------Substitute for x in A.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=12%28360%2Fz%5E2%29z%2Bz%5E2 ALIGN=MIDDLE  ALT=\"A=12%28360%2Fz%5E2%29z%2Bz%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28A=4320%2Fz%2Bz%5E2%29 ALIGN=MIDDLE  ALT=\"highlight%28A=4320%2Fz%2Bz%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-------Variable z must be used, take derivative, and find what makes A the minimum, and then find the corresponding x value, the asked for  length.\r<BR>\n" );
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document.write( "---------<BR>\n" );
document.write( "continuing,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=4320%2Fz%2Bz%5E2 ALIGN=MIDDLE  ALT=\"A=4320%2Fz%2Bz%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dA%2Fdz=2z-4320%2Fz%5E2 ALIGN=MIDDLE  ALT=\"dA%2Fdz=2z-4320%2Fz%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  You fill in the steps to that.\r<BR>\n" );
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document.write( "Set deriv to 0.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2z%28z%5E2%29%2Fz%5E2-4320%2Fz%5E2=0 ALIGN=MIDDLE  ALT=\"2z%28z%5E2%29%2Fz%5E2-4320%2Fz%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=%282z%5E3-4320%29%2Fz%5E2=0 ALIGN=MIDDLE  ALT=\"%282z%5E3-4320%29%2Fz%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The denominator does not take meaning here ...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2z%5E3-4320=0 ALIGN=MIDDLE  ALT=\"2z%5E3-4320=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E3-2160=0 ALIGN=MIDDLE  ALT=\"z%5E3-2160=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E3=2160 ALIGN=MIDDLE  ALT=\"z%5E3=2160\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and you can fill-in the steps...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28z=6sqrt%2810%29%29 ALIGN=MIDDLE  ALT=\"highlight%28z=6sqrt%2810%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Again use the equations from the description to reach the corresponding value for x, the length.<BR>\n" );
document.write( " </SPAN>\n" );
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