document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=988552>Question 988552</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2.  The  members  of  a  group  of  packaging  designers  of  a  gift  shop  are  looking for  a  precise  procedure  to  make  an  open  rectangular  box  with  a  volume  of 560  cubic  inches  from  a  24-inch  by  18-inch  rectangular  piece  of  material. The  main  problem  is  how  to  identify  the  side  of  identical  squares  to  be  cut from  the  four  corners  of  the  rectangular  sheet  so  that  such  box  can  be made </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #609071 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39628)</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=609071\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> w and L are the KNOWN width and length of the rectangular material.  x is the side length of each square to remove to form the open top box.  x is UNKNOWN.  The volume V of the box is KNOWN.\r<BR>\n" );
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document.write( "You would have  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28V=560%2CL=24%2Cw=18%29 ALIGN=MIDDLE  ALT=\"system%28V=560%2CL=24%2Cw=18%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The boxes base area is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28w-2x%29%28L-2x%29 ALIGN=MIDDLE  ALT=\"%28w-2x%29%28L-2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The height of the box is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The volume will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28x%28w-2x%29%28L-2x%29=V%29 ALIGN=MIDDLE  ALT=\"highlight_green%28x%28w-2x%29%28L-2x%29=V%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Begin simplifying.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28wL-2Lx-2wx%2B4x%5E2%29-V=0 ALIGN=MIDDLE  ALT=\"x%28wL-2Lx-2wx%2B4x%5E2%29-V=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E3-2Lx%5E2-2wx%5E2%2BwLx-V=0 ALIGN=MIDDLE  ALT=\"4x%5E3-2Lx%5E2-2wx%5E2%2BwLx-V=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This being a cubic equation very likely to be handled with Rational Roots Theorem or maybe graphing software, substituting the known values and simplifying the equation with those calculations is the next thing to do.\r<BR>\n" );
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document.write( "You can continue this from here hopefully. </SPAN>\n" );
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