document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1072574>Question 1072574</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular storage bin is to be made from a rectangular piece of sheet metal 16 in. by 14 &#8203;in., by cutting out equal corners of side x and bending up the&#8203; sides. Explain how to determine the maximum possible capacity for a storage bin constructed in this way. What is the maximum possible&#8203; capacity? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #687542 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=687542\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> v is volume as a function of x; x is the length of corner square to remove.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=%2816-2x%29%2814-2x%29x ALIGN=MIDDLE  ALT=\"v=%2816-2x%29%2814-2x%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Simplify v into general form through multiplications.  Find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dv%2Fdx ALIGN=MIDDLE  ALT=\"dv%2Fdx\"   DISABLED_style= \"max-width:90%; height:auto;\" >, equate to 0 and look for local maximum.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=224x-60x%5E2%2B4x%5E3 ALIGN=MIDDLE  ALT=\"v=224x-60x%5E2%2B4x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dv%2Fdx=224-120x%2B12x%5E2 ALIGN=MIDDLE  ALT=\"dv%2Fdx=224-120x%2B12x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Set to 0.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x%5E2-120x%2B224=0 ALIGN=MIDDLE  ALT=\"12x%5E2-120x%2B224=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2-30x%2B56=0 ALIGN=MIDDLE  ALT=\"3x%5E2-30x%2B56=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2830%2B-+sqrt%28228%29%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"x=%2830%2B-+sqrt%28228%29%29%2F%282%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2830%2B-+12%2Asqrt%282%29%29%2F6 ALIGN=MIDDLE  ALT=\"x=%2830%2B-+12%2Asqrt%282%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28x=5-2%2Asqrt%282%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28x=5-2%2Asqrt%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x to get maximum v </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );