document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1028760>Question 1028760</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular box is to have a square base and a volume of 40 ft3. If the material for the base costs $0.35/ft2, the material for the sides costs $0.05/ft2, and the material for the top costs $0.15/ft2, determine the dimensions of the box that can be constructed at minimum cost.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #643973 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=643973\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A rectangular box is to have a square base and a volume of 40 ft3.<BR>\n" );
document.write( " If the material for the base costs $0.35/ft2, the material for the sides costs $0.05/ft2, and the material for the top costs $0.15/ft2, determine the dimensions of the box that can be constructed at minimum cost.<BR>\n" );
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document.write( "let x = the length of the side of the square base<BR>\n" );
document.write( "then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2Fx%5E2 ALIGN=MIDDLE  ALT=\"40%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the height of the box<BR>\n" );
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document.write( "Area of the top and bottom will be x^2<BR>\n" );
document.write( "Area of each of the 4 sides will be :<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2840%2Fx%5E2%29 ALIGN=MIDDLE  ALT=\"x%2840%2Fx%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2Fx ALIGN=MIDDLE  ALT=\"40%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Fours sides area: 4*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2Fx ALIGN=MIDDLE  ALT=\"40%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=160%2Fx ALIGN=MIDDLE  ALT=\"160%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The cost equation<BR>\n" );
document.write( "Cost = base cost + side cost + top cost<BR>\n" );
document.write( "C(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.35x%5E2+%2B+.05%28160%2Fx%29+%2B+.15x%5E2 ALIGN=MIDDLE  ALT=\".35x%5E2+%2B+.05%28160%2Fx%29+%2B+.15x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "C(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.50x%5E2+%2B+8%2Fx ALIGN=MIDDLE  ALT=\".50x%5E2+%2B+8%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Graph this equation to find the min cost<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-2%2C+5%2C+-4%2C+20%2C+.5x%5E2%2B%288%2Fx%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-2%2C+5%2C+-4%2C+20%2C+.5x%5E2%2B%288%2Fx%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "minimum cots occurs when x = 1.7 ft, the length and width of the box<BR>\n" );
document.write( "Find the height<BR>\n" );
document.write( "h = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2F1.7%5E2 ALIGN=MIDDLE  ALT=\"40%2F1.7%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "h = 13.8 ft<BR>\n" );
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document.write( "The box dimension for min cost: 1.7 by 1.7 by 13.8 </SPAN>\n" );
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