document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=449938>Question 449938</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You are given one scrapbook page (12 inches by 12 inches). With only this for your material, you must create a container<BR>\n" );
document.write( "that will maximize volume while minimizing the total area. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #309518 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=309518\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I think the answer might be to cut 4 x 4 inch squares out of each corner.<BR>\n" );
document.write( "If you then fold the sides up, you have a 4 x 4 x 4 box open on top.<BR>\n" );
document.write( "the volume is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4%2A4%2A4+=+64+ ALIGN=MIDDLE  ALT=\"+4%2A4%2A4+=+64+\"   DISABLED_style= \"max-width:90%; height:auto;\" > in3<BR>\n" );
document.write( "The area is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5%2A4%2A4+=+80+ ALIGN=MIDDLE  ALT=\"+5%2A4%2A4+=+80+\"   DISABLED_style= \"max-width:90%; height:auto;\" > in2<BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "Call the squares cut out of the corners <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+ ALIGN=MIDDLE  ALT=\"+x%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The surface area is then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+144+-+4x%5E2+ ALIGN=MIDDLE  ALT=\"+A+=+144+-+4x%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > in2<BR>\n" );
document.write( "The volume is then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2A+%2812+-+2x%29%5E2+ ALIGN=MIDDLE  ALT=\"x%2A+%2812+-+2x%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------------------<BR>\n" );
document.write( "Suppose I removed  3.99 x 3.99 in2 from each corner<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+3.99%2A+%2812+-+2%2A3.99%29%5E2+ ALIGN=MIDDLE  ALT=\"V+=+3.99%2A+%2812+-+2%2A3.99%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+3.99%2A+%2812+-+7.98%29%5E2+ ALIGN=MIDDLE  ALT=\"V+=+3.99%2A+%2812+-+7.98%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+3.99%2A+4.02%5E2+ ALIGN=MIDDLE  ALT=\"V+=+3.99%2A+4.02%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+V+=+64.48+ ALIGN=MIDDLE  ALT=\"+V+=+64.48+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+144+-+4%2A15.92+ ALIGN=MIDDLE  ALT=\"+A+=+144+-+4%2A15.92+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+144+-+63.68+ ALIGN=MIDDLE  ALT=\"+A+=+144+-+63.68+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+80.32+ ALIGN=MIDDLE  ALT=\"+A+=+80.32+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Both volume and area went up.<BR>\n" );
document.write( "Now try <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+4.01+ ALIGN=MIDDLE  ALT=\"+x+=+4.01+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If either volume goes down or area goes up,<BR>\n" );
document.write( "my guess is right </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );