document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1151022>Question 1151022</A>: <I><SPAN STYLE=\"word-break: break-all;\"> . In the United Parcel Services example at the beginning , the length plus girth of a package was restricted to 108 inches. Suppose a shipper uses rectangular boxes with square ends made of a perforated material to provide ventilation, the shipper wants the total surface area to be as large as possible. Use x as the side of the square base and L as the length.<BR>\n" );
document.write( "a) Write the expression for the area, A, in terms of L and x.<BR>\n" );
document.write( "b) Express A(x) as a function of x alone.<BR>\n" );
document.write( "c) What value of x maximizes A(x)? Prove this is a maximum.<BR>\n" );
document.write( "d) What are the dimensions of the maximum-area box?<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 #772613 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=772613\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If \"restricted to\" means equal to then the system of equations <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28L%2B4x=108%2CA=2x%5E2%2B4Lx%29 ALIGN=MIDDLE  ALT=\"system%28L%2B4x=108%2CA=2x%5E2%2B4Lx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >   fits the description.\r<BR>\n" );
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document.write( "Substituting and simplifying gives <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=432x-14x%5E2 ALIGN=MIDDLE  ALT=\"A=432x-14x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dA%2Fdx=432-28x=0 ALIGN=MIDDLE  ALT=\"dA%2Fdx=432-28x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=108-7x=0 ALIGN=MIDDLE  ALT=\"108-7x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=108=7x ALIGN=MIDDLE  ALT=\"108=7x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=15.43%29 ALIGN=MIDDLE  ALT=\"highlight%28x=15.43%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=inches ALIGN=MIDDLE  ALT=\"inches\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=108-4x ALIGN=MIDDLE  ALT=\"L=108-4x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=108-4%2A15.43 ALIGN=MIDDLE  ALT=\"L=108-4%2A15.43\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28L=46.29%29 ALIGN=MIDDLE  ALT=\"highlight%28L=46.29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=inches ALIGN=MIDDLE  ALT=\"inches\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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