document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=907313>Question 907313</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular storage container with an open top is to have a volume of 10 m3. The length of this base is twice the width. Material for the base costs $20 per square meter. Material for the sides costs $12 per square meter. Find the cost of materials for the cheapest such container. (Round your answer to the nearest cent.)\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 #550238 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</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=550238\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x for length, y for width,<BR>\n" );
document.write( "x=2y<BR>\n" );
document.write( "volume is 10 cubic meters, so if for z height,<BR>\n" );
document.write( "xyz=10\r<BR>\n" );
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document.write( "Finding z:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282y%29yz=10 ALIGN=MIDDLE  ALT=\"%282y%29yz=10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y%5E2%2Az=10 ALIGN=MIDDLE  ALT=\"2y%5E2%2Az=10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Still more information is needed to have a better relationship among the three dimensions.\r<BR>\n" );
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document.write( "These are the costs of the different rectangular parts altogether:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy%2A20%2B2%2Axz%2A12%2B2%2Ayz%2A12 ALIGN=MIDDLE  ALT=\"xy%2A20%2B2%2Axz%2A12%2B2%2Ayz%2A12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20xy%2B24xz%2B24yz ALIGN=MIDDLE  ALT=\"20xy%2B24xz%2B24yz\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and if you substitute for y,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%282y%29y%2B24%282y%29%2B24yz ALIGN=MIDDLE  ALT=\"20%282y%29y%2B24%282y%29%2B24yz\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40y%5E2%2B48y%2B24yz ALIGN=MIDDLE  ALT=\"40y%5E2%2B48y%2B24yz\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----This cost written in terms of y and z.\r<BR>\n" );
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document.write( "You can use the earlier found, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y%5E2%2Az=10 ALIGN=MIDDLE  ALT=\"2y%5E2%2Az=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > to either substitute for y or for z in the cost function.<BR>\n" );
document.write( "First, simplify the \"10\" equation to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%2Ay%5E2=5 ALIGN=MIDDLE  ALT=\"z%2Ay%5E2=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=5%2Fy%5E2 ALIGN=MIDDLE  ALT=\"z=5%2Fy%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >; substitute for z, done here.\r<BR>\n" );
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document.write( "cost, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40y%5E2%2B48y%2B24y%285%2Fy%5E2%29 ALIGN=MIDDLE  ALT=\"40y%5E2%2B48y%2B24y%285%2Fy%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28c%28y%29=40y%5E2%2B48y%2B120%2Fy%29 ALIGN=MIDDLE  ALT=\"highlight_green%28c%28y%29=40y%5E2%2B48y%2B120%2Fy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "This is probably meant as a calculus problem using the derivative <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dc%2Fdy ALIGN=MIDDLE  ALT=\"dc%2Fdy\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Form the derivative, and solve for y in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dc%2Fdy=0 ALIGN=MIDDLE  ALT=\"dc%2Fdy=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find and check extremes (for a minimum value for c).<BR>\n" );
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