document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=443207>Question 443207</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a company wishes to manufacture a box with a volume of 36 cubic feet that is open on top and is twice as long as it is wide.  find the dimensions of the box produced from the minimum amount 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 #305902 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=305902\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> On thinking this over last night, I discovered a big error in this, let me correct it here<BR>\n" );
document.write( "//////////////////////////<BR>\n" );
document.write( "a company wishes to manufacture a box with a volume of 36 cubic feet that is open on top and is twice as long as it is wide.<BR>\n" );
document.write( " find the dimensions of the box produced from the minimum amount of material.<BR>\n" );
document.write( "Let x = the width <BR>\n" );
document.write( "Let 2x = the length<BR>\n" );
document.write( "Let h = the height <BR>\n" );
document.write( "then<BR>\n" );
document.write( "vol = x*2x*h<BR>\n" );
document.write( "so we have<BR>\n" );
document.write( "2x^2*h = 36<BR>\n" );
document.write( "h = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36%2F%282x%5E2%29 ALIGN=MIDDLE  ALT=\"36%2F%282x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "h = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2Fx%5E2 ALIGN=MIDDLE  ALT=\"18%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Surface area: two ends + 1 bottom + 2 sides (no top)<BR>\n" );
document.write( "S.A. = 2(x*h) + 1(2x*x) + 2(2x*h)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "I am truly sorry for this error.  Carl<BR>\n" );
document.write( ":<BR>\n" );
document.write( "S.A. = 2xh + 2x^2 + 4xh<BR>\n" );
document.write( "S.A. = 2x^2 + 6xh<BR>\n" );
document.write( "Replace h with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2Fx%5E2 ALIGN=MIDDLE  ALT=\"18%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "S.A = 2x^2 + 6x(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2Fx%5E2 ALIGN=MIDDLE  ALT=\"18%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "S.A = 2x^2 + 6(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2Fx ALIGN=MIDDLE  ALT=\"18%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "S.A = 2x^2 + (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=108%2Fx ALIGN=MIDDLE  ALT=\"108%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "Graph this equation to find the value of x for minimum material<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-1%2C+5%2C+-20%2C+150%2C+2x%5E2%2B%28108%2Fx%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-1%2C+5%2C+-20%2C+150%2C+2x%5E2%2B%28108%2Fx%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Min surface area when x = 3.0 is the width<BR>\n" );
document.write( "then<BR>\n" );
document.write( "2(3) = 6 is the length<BR>\n" );
document.write( ";<BR>\n" );
document.write( "Find the height:<BR>\n" );
document.write( "h = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2F3%5E2 ALIGN=MIDDLE  ALT=\"18%2F3%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "h = 2<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Box dimensions for min surface area: 3 by 6 by 2; much better numbers<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check the vol of these dimensions: 3*6*2 ~ 36 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );