document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1075632>Question 1075632</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A closed box with square base is to be built to house an ant colony. The bottom of the box and all four sides are to be made of material costing $2/ft2, and the top is to be constructed of glass costing $4/ft2. What are the dimensions of the box of greatest volume that can be constructed for $72? (Enter the dimensions (in feet) as a comma separated list.) \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #690294 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=690294\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let each of the 2 base dimensions = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+ ALIGN=MIDDLE  ALT=\"+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let the height dimension = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+ ALIGN=MIDDLE  ALT=\"+y+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The area of the 4 sides = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4%2Ax%2Ay+ ALIGN=MIDDLE  ALT=\"+4%2Ax%2Ay+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The area of the base = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+ ALIGN=MIDDLE  ALT=\"+x%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The area of the top is also <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+ ALIGN=MIDDLE  ALT=\"+x%5E2+\"   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=+2%2A%28+x%5E2+%2B+4%2Ax%2Ay+%29+%2B+4%2Ax%5E2+=+72+ ALIGN=MIDDLE  ALT=\"+2%2A%28+x%5E2+%2B+4%2Ax%2Ay+%29+%2B+4%2Ax%5E2+=+72+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x%5E2+%2B+8%2Ax%2Ay+%2B+4x%5E2+=+72+ ALIGN=MIDDLE  ALT=\"+2x%5E2+%2B+8%2Ax%2Ay+%2B+4x%5E2+=+72+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+8%2Ax%2Ay++=+72+-+6x%5E2+ ALIGN=MIDDLE  ALT=\"+8%2Ax%2Ay++=+72+-+6x%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+=+9%2Fx+-+%283%2F4%29%2Ax+ ALIGN=MIDDLE  ALT=\"+y+=+9%2Fx+-+%283%2F4%29%2Ax+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( "The volume is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+V+=+x%5E2%2A%28+9%2Fx+-+%283%2F4%29%2Ax+%29+ ALIGN=MIDDLE  ALT=\"+V+=+x%5E2%2A%28+9%2Fx+-+%283%2F4%29%2Ax+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+V+=+9x+-+%283%2F4%29%2Ax%5E3+ ALIGN=MIDDLE  ALT=\"+V+=+9x+-+%283%2F4%29%2Ax%5E3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------------------<BR>\n" );
document.write( "If volume <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+V+ ALIGN=MIDDLE  ALT=\"+V+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is maximized, then the cost of<BR>\n" );
document.write( "construction will still be $72 total.<BR>\n" );
document.write( "I will assume that this is a calculus problem, and<BR>\n" );
document.write( "I will set the slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+V+ ALIGN=MIDDLE  ALT=\"+V+\"   DISABLED_style= \"max-width:90%; height:auto;\" > equal to zero.<BR>\n" );
document.write( "slope = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+9+-+%289%2F4%29%2Ax%5E2+=+0+ ALIGN=MIDDLE  ALT=\"+9+-+%289%2F4%29%2Ax%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=+%289%2F4%29%2Ax%5E2+=+9+ ALIGN=MIDDLE  ALT=\"+%289%2F4%29%2Ax%5E2+=+9+\"   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+=+4+ ALIGN=MIDDLE  ALT=\"+x%5E2+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+2+ ALIGN=MIDDLE  ALT=\"+x+=+2+\"   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+=+9%2Fx+-+%283%2F4%29%2Ax+ ALIGN=MIDDLE  ALT=\"+y+=+9%2Fx+-+%283%2F4%29%2Ax+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+9%2F2+-+%283%2F4%29%2A2+ ALIGN=MIDDLE  ALT=\"+y+=+9%2F2+-+%283%2F4%29%2A2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+4.5+-+1.5+ ALIGN=MIDDLE  ALT=\"+y+=+4.5+-+1.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+3+ ALIGN=MIDDLE  ALT=\"+y+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The dimensions in feet are:<BR>\n" );
document.write( "2,2,3<BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "check answer:<BR>\n" );
document.write( "Here's the plot of volume, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+V+ ALIGN=MIDDLE  ALT=\"+V+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, on vertical axis<BR>\n" );
document.write( "and base dimension, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+ ALIGN=MIDDLE  ALT=\"+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, on the horizontal axis.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-5%2C+5%2C+-20%2C+20%2C+9x+-+%283%2F4%29%2Ax%5E3++%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-5%2C+5%2C+-20%2C+20%2C+9x+-+%283%2F4%29%2Ax%5E3++%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "It looks like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+V+ ALIGN=MIDDLE  ALT=\"+V+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is maximized when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+2+ ALIGN=MIDDLE  ALT=\"+x+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "Get a 2nd opinion if needed<BR>\n" );
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