document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1099943>Question 1099943</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A box is constructed out of two different types of metal. The metal for the top and bottom, which are both square, costs $5 per square foot and the metal for the sides costs $2 per square foot. Find the dimensions that minimize cost if the box has a volume of 15 cubic feet. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #714545 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=714545\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A box is constructed out of two different types of metal.<BR>\n" );
document.write( " The metal for the top and bottom, which are both square, costs $5 per square foot and the metal for the sides costs $2 per square foot.<BR>\n" );
document.write( " Find the dimensions that minimize cost if the box has a volume of 15 cubic feet.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "let s = one side of the square base<BR>\n" );
document.write( "let h = the height of the box<BR>\n" );
document.write( "then<BR>\n" );
document.write( "s^2 * h = 15 cu/ft<BR>\n" );
document.write( "Therefore<BR>\n" );
document.write( "h = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2Fs%5E2 ALIGN=MIDDLE  ALT=\"15%2Fs%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "surface area = top, bottom, 4 side areas<BR>\n" );
document.write( "SA = 2s^2 + 4hs<BR>\n" );
document.write( "replace h with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2Fs%5E2 ALIGN=MIDDLE  ALT=\"15%2Fs%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "SA = 2s^2 + 4s*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2Fs%5E2 ALIGN=MIDDLE  ALT=\"15%2Fs%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "cancel the s<BR>\n" );
document.write( "SA = 2s^2 + (60/s)<BR>\n" );
document.write( "Cost of the box<BR>\n" );
document.write( "C(x) = 5(2x^2) + 2(60/s)<BR>\n" );
document.write( "C(x) = 10x^2 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120%2Fs ALIGN=MIDDLE  ALT=\"120%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "Graphically, y axis = the cost<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-3%2C+5%2C+-20%2C+160%2C+10x%5E2%2B%28120%2Fx%29%2C+99.26%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-3%2C+5%2C+-20%2C+160%2C+10x%5E2%2B%28120%2Fx%29%2C+99.26%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "minimum cost when x=1.9 ft<BR>\n" );
document.write( "find the height<BR>\n" );
document.write( "h = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2F1.9%5E2 ALIGN=MIDDLE  ALT=\"15%2F1.9%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "h = 4.155 ft<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The dimensions for minimum cost: 1.9 by 1.9 by 4.155 ft Cost about $99.26 (green)<BR>\n" );
document.write( " <BR>\n" );
document.write( "   </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );