document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1086801>Question 1086801</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An open-top box with a square base is to be made from two materials, one for the bottom and one for the sides. The volume of a box is to be 18 cubic feet. The cost of material for the bottom is P10.00 per square foot and the cost of the material for the sides is P7.00 per square foot. determine a model for the cost of the box as a function of its height h. what is the domain of the function? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #701073 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=701073\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An open-top box with a square base is to be made from two materials, one for the bottom and one for the sides.<BR>\n" );
document.write( "let s = the side of the square base<BR>\n" );
document.write( "let h = the height of the box<BR>\n" );
document.write( " The volume of a box is to be 18 cubic feet.<BR>\n" );
document.write( "s * s * h = 18<BR>\n" );
document.write( "s^2 * h = 18<BR>\n" );
document.write( "s^2 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2Fh ALIGN=MIDDLE  ALT=\"18%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "s = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2818%2Fh%29 ALIGN=MIDDLE  ALT=\"sqrt%2818%2Fh%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " The cost of material for the bottom is P10.00 per square foot and the cost of the material for the sides is P7.00 per square foot<BR>\n" );
document.write( "Surface area:<BR>\n" );
document.write( "S.A. = s^2 + 4(s*h)<BR>\n" );
document.write( "Cost = 10s^2 + 7(4s*h)<BR>\n" );
document.write( "C = 10s^2 + 28s*h<BR>\n" );
document.write( "determine a model for the cost of the box as a function of its height h. <BR>\n" );
document.write( "Replace s with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2818%2Fh%29 ALIGN=MIDDLE  ALT=\"sqrt%2818%2Fh%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "C(h) = 10<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2818%2Fh%29%29%5E2 ALIGN=MIDDLE  ALT=\"sqrt%2818%2Fh%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 28*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2818%2Fh%29 ALIGN=MIDDLE  ALT=\"sqrt%2818%2Fh%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >*h<BR>\n" );
document.write( "C(h) = 10(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2Fh ALIGN=MIDDLE  ALT=\"18%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" >) + 28*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2818%2Fh%29 ALIGN=MIDDLE  ALT=\"sqrt%2818%2Fh%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >*h<BR>\n" );
document.write( "simplify, extract the square root of 9<BR>\n" );
document.write( "C(h) = 10(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2Fh ALIGN=MIDDLE  ALT=\"18%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" >) + 28*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3sqrt%282%2Fh%29 ALIGN=MIDDLE  ALT=\"3sqrt%282%2Fh%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >*h<BR>\n" );
document.write( "C(h) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180%2Fh ALIGN=MIDDLE  ALT=\"180%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=84sqrt%282%2Fh%29 ALIGN=MIDDLE  ALT=\"84sqrt%282%2Fh%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >*h<BR>\n" );
document.write( ":<BR>\n" );
document.write( " what is the domain of the function, <BR>\n" );
document.write( "all positive values for h<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Looks like this, y = Cost; x = height<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-6%2C+20%2C+-100%2C+450%2C+%28180%2Fx%29+%2B+%2884sqrt%282%2Fx%29%2Ax%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "minimum cost when height = 2, the side of the square base = 3<BR>\n" );
document.write( "That would be 10(3^2) + 7(4*2*3) = $258  </SPAN>\n" );
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