document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1121065>Question 1121065</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a company wants to manufature gift boxes in the shape of rectangular prisms .each gift box will have a volume of 84 cubic inches the base of the rectangular prism shold be twice as long as it is wide.what dimensions should the company choose for the gift boxes in order to minimize the surface area of each box. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #736800 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=736800\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Width of base:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large w\">\r<BR>\n" );
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document.write( "Length of base:   <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 2w\">\r<BR>\n" );
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document.write( "Height of prism:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large h\">\r<BR>\n" );
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document.write( "Volume of prism:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large V(w,h)\ =\ 2w^2h\ =\ 84\">\r<BR>\n" );
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document.write( "Surface Area:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large S(w,h)\ =\ 4w^2\ +\ 4wh\ +\ 2wh\ =\ 4w^2\ +\ 6wh\">\r<BR>\n" );
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document.write( "But then:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large h\ =\ \frac{42}{w^2}\">\r<BR>\n" );
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document.write( "Hence the surface area as a function of the width is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large S(w)\ =\ 4w^2\ +\ \frac{252}{w}\">\r<BR>\n" );
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document.write( "And then the first derivative of the surface area function is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ S'(w)\ =\ 8w\ -\ \frac{252}{w^2}\">\r<BR>\n" );
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document.write( "Set the derivative equal to zero:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 8w\ -\ \frac{252}{w^2}\ =\ 0\">\r<BR>\n" );
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document.write( "Solve for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large w\">, then calculate <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 2w\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{42}{w}\"><BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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