document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=760994>Question 760994</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A closed rectangular box is to be constructed with a square base. The material for the top costs $2 per square foot whereas the material for the remaining sides costs $1 per square foot. If the total cost to construct each box is $36, express the volume of the box in terms of the width of the base. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #463000 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</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=463000\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The square bottom and top have a side length, w.  The rectangular box is height h.  Using w and h, the volume of the box is this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=h%2Aw%5E2 ALIGN=MIDDLE  ALT=\"v=h%2Aw%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The volume will also depend on the cost of the six sides making the box.  <BR>\n" );
document.write( "Top: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w%5E2%2A2 ALIGN=MIDDLE  ALT=\"+w%5E2%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" > dollars<BR>\n" );
document.write( "Bottom:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E2%2A1 ALIGN=MIDDLE  ALT=\"w%5E2%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" > dollar<BR>\n" );
document.write( "One side: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%2Aw%2A1 ALIGN=MIDDLE  ALT=\"h%2Aw%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cost of the box: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2w%5E2%2Bw%5E2%2B4hw=36 ALIGN=MIDDLE  ALT=\"2w%5E2%2Bw%5E2%2B4hw=36\"   DISABLED_style= \"max-width:90%; height:auto;\" >______see the factor 4 for the four sides.\r<BR>\n" );
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document.write( "We want v as a function of w.  We can get this solving the cost equation for h.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4hw=36-2w%5E2-w%5E2 ALIGN=MIDDLE  ALT=\"4hw=36-2w%5E2-w%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=36%2F%284w%29-3w%5E2%2F%284w%29 ALIGN=MIDDLE  ALT=\"h=36%2F%284w%29-3w%5E2%2F%284w%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=9%2Fw-%283%2F4%29w ALIGN=MIDDLE  ALT=\"h=9%2Fw-%283%2F4%29w\"   DISABLED_style= \"max-width:90%; height:auto;\" >______________Next, substitute this for h in the volume equation, v.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=%289%2Fw-%283%2F4%29w%29w%5E2 ALIGN=MIDDLE  ALT=\"v=%289%2Fw-%283%2F4%29w%29w%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28v=9w-%283%2F4%29w%5E3%29 ALIGN=MIDDLE  ALT=\"highlight%28v=9w-%283%2F4%29w%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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