document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1139325>Question 1139325</A>: <I><SPAN STYLE=\"word-break: break-all;\">  You are to construct an open box<BR>\n" );
document.write( "from a rectangular sheet of cardboard that measures 18<BR>\n" );
document.write( "inches by 25 inches. To assemble the box, you make the four<BR>\n" );
document.write( "cuts shown in the figure below and then fold on the dashed<BR>\n" );
document.write( "lines. What value of x (to the nearest 0.01 inch) will produce a<BR>\n" );
document.write( "box with maximum volume? What is the maximum volume (to<BR>\n" );
document.write( "the nearest 0.1 cubic inch)?\r<BR>\n" );
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document.write( "Figure: https://i.imgur.com/lPeHsph.png </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #757108 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=757108\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You are to construct an open box from a rectangular sheet of cardboard that measures 18 inches by 25 inches.<BR>\n" );
document.write( " To assemble the box, you make the four cuts shown in the figure below and then fold on the dashed lines.<BR>\n" );
document.write( " What value of x (to the nearest 0.01 inch) will produce a box with maximum volume?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "From the diagram we can see the dimensions will be (25-4x) by (18-2x) and the height will be x<BR>\n" );
document.write( "the volume then<BR>\n" );
document.write( "V = (25-4x)*(18-2x)*x<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "V = (450-50x-72x+8x^2)*x<BR>\n" );
document.write( "V = 8x^3 - 122x^2 + 450x<BR>\n" );
document.write( "We can plot this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-4%2C+8%2C+-100%2C+550%2C+8x%5E3+-+122x%5E2+%2B+450x%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-4%2C+8%2C+-100%2C+550%2C+8x%5E3+-+122x%5E2+%2B+450x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Max volume is when x = 2.41\" </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );