document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=936346>Question 936346</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An artist plans to construct an open box from 15 in. By 20 in. Sheet of met by cutting squares from the corners and folding up the sides. Sketch the graph that will show maximum volume of the box in terms of x.  \r<BR>\n" );
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document.write( "Define variables (represent length, width and height in terms of x)\r<BR>\n" );
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document.write( "Write a polynomial as the product of linear factors\r<BR>\n" );
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document.write( "Sketch the graph\r<BR>\n" );
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document.write( "Indicate where on the graph the maximum volume will be found  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #569781 by </B><A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><B>TimothyLamb(4379)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><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=TimothyLamb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=569781\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ---<BR>\n" );
document.write( "x = side length of corner squares<BR>\n" );
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document.write( "L = 20 - 2x<BR>\n" );
document.write( "w = 15 - 2x<BR>\n" );
document.write( "h = x<BR>\n" );
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document.write( "v = Lwh<BR>\n" );
document.write( "v = (20 - 2x)(15 - 2x)x<BR>\n" );
document.write( "v = (20*15 - 20*2x - 2*15x + 4xx)x<BR>\n" );
document.write( "v = 300x - 40xx - 30xx + 4xxx<BR>\n" );
document.write( "v = 4xxx - 70xx + 300x<BR>\n" );
document.write( "v = 4x^3 - 70x^2 + 300x<BR>\n" );
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document.write( "the graph:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-2%2C+12%2C+-100%2C+600%2C+4x%5E3-70x%5E2%2B300x%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-2%2C+12%2C+-100%2C+600%2C+4x%5E3-70x%5E2%2B300x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "maximum volume occurs at the graph peak, for x approximately = 2.831 inches<BR>\n" );
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document.write( "Solve systems of linear equations up to 6-equations 6-variables:<BR>\n" );
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