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 #736801 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=736801\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The volume of the rectangular prism is V = l*w*h = 84 in^3<BR>\n" );
document.write( "The area is A = 2(l*w + l*h + w*h)<BR>\n" );
document.write( "The base l is equal to twice the width: l = 2w<BR>\n" );
document.write( "Thus V = 2*w^2*h and A = 2(w^2 + 2wh + wh) = 2w(w + 3h)<BR>\n" );
document.write( "Expressing h in terms of w gives h = V/(2*w^2)<BR>\n" );
document.write( "Thus A = 2w(w + 3V/(2*w^2))<BR>\n" );
document.write( "The area will be minimized when dA/dw = 0<BR>\n" );
document.write( "0 = 4w - 3V/w^2 -> w = (3V/4)^(1/3)<BR>\n" );
document.write( "Substituting the value for V gives w = 3.979<BR>\n" );
document.write( "Therefore l = 7.958 and h = 84/(2*3.979^2) = 2.653 </SPAN>\n" );
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