document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=198713>Question 198713</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Mr. Greene has 8.5 in by 11 in cardboard sheets. As a class project, Mr. Greene asked each of his students to amke an open-top box under these conditions:<BR>\n" );
document.write( "I. Each box must be made by cutting small squares from each corner of a cardboard sheet.<BR>\n" );
document.write( "II. The box must have a volume of 48 in^3<BR>\n" );
document.write( "III. The amount of cardboard waste must be minimized.<BR>\n" );
document.write( "What is the appropriate side length for the small squares that would be cut from the cardboard sheet? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #149271 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=149271\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Mr. Greene has 8.5 in by 11 in cardboard sheets. As a class project, Mr. Greene<BR>\n" );
document.write( " asked each of his students to make an open-top box under these conditions:<BR>\n" );
document.write( ":<BR>\n" );
document.write( "I. Each box must be made by cutting small squares from each corner of a cardboard sheet.<BR>\n" );
document.write( "Let the side of the small square = x<BR>\n" );
document.write( "then<BR>\n" );
document.write( "the dimension of the box: (8.5-2x) by (11-2x) by x<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "x(93.5 - 17x - 22x +4x^2)<BR>\n" );
document.write( "A volume equation<BR>\n" );
document.write( "V = 4x^3 - 39x^2 + 93.5x <BR>\n" );
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document.write( "II. The box must have a volume of 48 in^3<BR>\n" );
document.write( "4x^3 - 39x^2 + 93.5x = 48<BR>\n" );
document.write( "4x^3 - 39x^2 + 93.5x - 48 = 0<BR>\n" );
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document.write( "III. The amount of cardboard waste must be minimized.<BR>\n" );
document.write( "Graph the above equation to find the values of x:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-2%2C+4%2C+-10%2C+50%2C+4x%5E3-39x%5E2%2B93.5x-48%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-2%2C+4%2C+-10%2C+50%2C+4x%5E3-39x%5E2%2B93.5x-48%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "What is the appropriate side length for the small squares that would be<BR>\n" );
document.write( " cut from the cardboard sheet?<BR>\n" );
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document.write( "The smaller solution: x ~.7\"; would give us the smallest removed squares<BR>\n" );
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document.write( "Check our solution: 2x = 1.4<BR>\n" );
document.write( "(8.5-1.4) * (11-1.4) * .7 =<BR>\n" );
document.write( "7.1 * 9.6 * .7 = 47.4 ~ 48 </SPAN>\n" );
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