document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1058007>Question 1058007</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular storage container with an open top is to have a volume of 12 cubic meters. The length of its base is twice the width. Material for the base costs 13 dollars per square meter. Material for the sides costs 7 dollars per square meter. Find the cost of materials for the cheapest such container.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #673067 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=673067\">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=+h+ ALIGN=MIDDLE  ALT=\"+h+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the height of the box<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w+ ALIGN=MIDDLE  ALT=\"+w+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the width<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2w+ ALIGN=MIDDLE  ALT=\"+2w+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the length<BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "The cost of the base is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2w%2Aw%2A13+ ALIGN=MIDDLE  ALT=\"+2w%2Aw%2A13+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+26w%5E2+ ALIGN=MIDDLE  ALT=\"+26w%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "The area of the sides is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2Aw%2Ah+%2B+2%2A%28+2w+%29%2Ah+ ALIGN=MIDDLE  ALT=\"+2%2Aw%2Ah+%2B+2%2A%28+2w+%29%2Ah+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2w%2Ah+%2B+4w%2Ah+=+6w%2Ah+ ALIGN=MIDDLE  ALT=\"+2w%2Ah+%2B+4w%2Ah+=+6w%2Ah+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The cost of the materials for sides is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6w%2Ah%2A7+=+42w%2Ah+ ALIGN=MIDDLE  ALT=\"+6w%2Ah%2A7+=+42w%2Ah+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------------------<BR>\n" );
document.write( "Also given:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w%2A2w%2Ah+=+12+ ALIGN=MIDDLE  ALT=\"+w%2A2w%2Ah+=+12+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2w%5E2h+=+12+ ALIGN=MIDDLE  ALT=\"+2w%5E2h+=+12+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h+=+12%2F%28+2w%5E2+%29+ ALIGN=MIDDLE  ALT=\"+h+=+12%2F%28+2w%5E2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C+ ALIGN=MIDDLE  ALT=\"+C+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = cost of materials<BR>\n" );
document.write( "The cost for materials is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+26w%5E2+%2B+42w%2Ah+ ALIGN=MIDDLE  ALT=\"+26w%5E2+%2B+42w%2Ah+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+26w%5E2+%2B+42w%2A%28+12%2F%28+2w%5E2+%29+%29+ ALIGN=MIDDLE  ALT=\"+26w%5E2+%2B+42w%2A%28+12%2F%28+2w%5E2+%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C+=+26w%5E2+%2B+252%2Fw+ ALIGN=MIDDLE  ALT=\"+C+=+26w%5E2+%2B+252%2Fw+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------------------------<BR>\n" );
document.write( "I don't know if this is for a calculus course, but<BR>\n" );
document.write( "that's the only way I can solve it.<BR>\n" );
document.write( "Take the derivative and set  = zero<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+52w+-+252%2Fw%5E2+=+0+ ALIGN=MIDDLE  ALT=\"+52w+-+252%2Fw%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=+52w+=+252%2Fw%5E2+ ALIGN=MIDDLE  ALT=\"+52w+=+252%2Fw%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+52w%5E3+=+252+ ALIGN=MIDDLE  ALT=\"+52w%5E3+=+252+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w%5E3+=+4.8462+ ALIGN=MIDDLE  ALT=\"+w%5E3+=+4.8462+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w+=+1.6923+ ALIGN=MIDDLE  ALT=\"+w+=+1.6923+\"   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=+C%5B+min+%5D+=+26w%5E2+%2B+252%2Fw+ ALIGN=MIDDLE  ALT=\"+C%5B+min+%5D+=+26w%5E2+%2B+252%2Fw+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C%5B+min+%5D+=+26%2A1.6923%5E2+%2B+252%2F1.6923+ ALIGN=MIDDLE  ALT=\"+C%5B+min+%5D+=+26%2A1.6923%5E2+%2B+252%2F1.6923+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C%5B+min+%5D+=+74.4573+%2B+148.9098+ ALIGN=MIDDLE  ALT=\"+C%5B+min+%5D+=+74.4573+%2B+148.9098+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C%5Bmin%5D+=+223.367+ ALIGN=MIDDLE  ALT=\"+C%5Bmin%5D+=+223.367+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The minimum cost is $223.37<BR>\n" );
document.write( "------------------------------<BR>\n" );
document.write( "Check:<BR>\n" );
document.write( "Is the 2nd derivative positive? ( that makes it a min )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+52+-+252%2A%28-2%29%2Fw%5E3+ ALIGN=MIDDLE  ALT=\"+52+-+252%2A%28-2%29%2Fw%5E3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+52+%2B+504%2Fw%5E3+ ALIGN=MIDDLE  ALT=\"+52+%2B+504%2Fw%5E3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > yes, it's positive<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=+C%28w%29+ ALIGN=MIDDLE  ALT=\"+C%28w%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+-2%2C+10%2C+-400%2C+400%2C+26x%5E2+%2B+252%2Fx+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-2%2C+10%2C+-400%2C+400%2C+26x%5E2+%2B+252%2Fx+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "I may have the right answer. Get another opinion on this\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );