document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1128128>Question 1128128</A>: <I><SPAN STYLE=\"word-break: break-all;\">  A rectangular storage container with an open top is to have a volume of 18 cubic meters. The length of its base is twice the width. Material for the base costs 10 dollars per square meter. Material for the sides costs 8 dollars per square meter. Find the cost of materials for the cheapest such container. <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #744680 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=744680\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A rectangular storage container with an open top is to have a volume of 18 cubic meters.<BR>\n" );
document.write( " The length of it's base is twice the width.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "let x = the width of the base<BR>\n" );
document.write( "then<BR>\n" );
document.write( "2x = the length of the base<BR>\n" );
document.write( "and<BR>\n" );
document.write( "h = height of the box<BR>\n" );
document.write( ":<BR>\n" );
document.write( "2x^2 = the area of the base<BR>\n" );
document.write( "2(2xh) = 4xh = area of the two vertical sides<BR>\n" );
document.write( "2xh = area of the two other vertical sides<BR>\n" );
document.write( "then<BR>\n" );
document.write( "4xh + 2xh = 6xh, the area of the 4 vertical sides\r<BR>\n" );
document.write( "\n" );
document.write( "The volume equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2Ah+=+18 ALIGN=MIDDLE  ALT=\"2x%5E2%2Ah+=+18\"   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%2F%282x%5E2%29 ALIGN=MIDDLE  ALT=\"18%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=9%2Fx%5E2 ALIGN=MIDDLE  ALT=\"9%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( " Material for the base costs 10 dollars per square meter.<BR>\n" );
document.write( " Material for the sides costs 8 dollars per square meter.<BR>\n" );
document.write( " Find the cost of materials for the cheapest such container.<BR>\n" );
document.write( "Cost equation<BR>\n" );
document.write( "C = 10(2x^2) + 8(6xh)<BR>\n" );
document.write( "C = 20x^2 + 48xh<BR>\n" );
document.write( "Replace h with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2F%282x%5E2%29 ALIGN=MIDDLE  ALT=\"18%2F%282x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "C(x) = 20x^2 + 48x(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F%28x%5E2%29 ALIGN=MIDDLE  ALT=\"9%2F%28x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "Cancel x<BR>\n" );
document.write( "C(x) = 20x^2 + 48(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2Fx ALIGN=MIDDLE  ALT=\"9%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "C(x) = 20x^2 + (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=432%2Fx ALIGN=MIDDLE  ALT=\"432%2Fx\"   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=+graph%28+300%2C+200%2C+-2%2C+4%2C+-100%2C+400%2C+%2820x%5E2%29%2B%28432%2Fx%29+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-2%2C+4%2C+-100%2C+400%2C+%2820x%5E2%29%2B%28432%2Fx%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "minimum cost:<BR>\n" );
document.write( " x = 2.25 meters is the width of the base<BR>\n" );
document.write( "and<BR>\n" );
document.write( "2(2.25) = 4.5 meters is the length of the base<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=9%2F%282.25%5E2%29 ALIGN=MIDDLE  ALT=\"9%2F%282.25%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=9%2F5.0625 ALIGN=MIDDLE  ALT=\"9%2F5.0625\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " h = 1.78 meters is the height<BR>\n" );
document.write( ":<BR>\n" );
document.write( "cost of the open box<BR>\n" );
document.write( "C = 10(4.5*2.25) + 8(6*2.25*1.78)<BR>\n" );
document.write( "C = 10(10.125) + 8(24)<BR>\n" );
document.write( "C = 101.25 + 192<BR>\n" );
document.write( "C = $293.25 the min cost for an open box which is: 2.25 by 4.5 by 1.78 m </SPAN>\n" );
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