document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201504>Question 1201504</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An aquarium that holds 40 cubic meters of water is to be made such that the length of its base is twice the width. If material for the base costs $20 per square meter, and the material for the sides costs $16 per square meter, find the cost of the materials for the cheapest such aquarium. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #835912 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=835912\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An aquarium that holds 40 cubic meters of water<BR>\n" );
document.write( " L*w*h = 40<BR>\n" );
document.write( "is to be made such that the length of its base is twice the width.<BR>\n" );
document.write( " L = 2w<BR>\n" );
document.write( "therefore if we replace L with 2w<BR>\n" );
document.write( " 2w^2h = 40<BR>\n" );
document.write( "divide eq by 2<BR>\n" );
document.write( " w^2h = 20<BR>\n" );
document.write( "or<BR>\n" );
document.write( "h = 20/(w^2)<BR>\n" );
document.write( "If material for the base costs $20 per square meter,<BR>\n" );
document.write( " 20(L*w)<BR>\n" );
document.write( "replace L with 2w<BR>\n" );
document.write( " 20(2w^2 = 40w^2 is cost of the base<BR>\n" );
document.write( "and the material for the sides costs $16 per square meter,<BR>\n" );
document.write( " 16(2(L*h)<BR>\n" );
document.write( " 32Lh<BR>\n" );
document.write( "replace L with 2w<BR>\n" );
document.write( " 32(2wh) = 64wh is the cost of the long sides<BR>\n" );
document.write( "and<BR>\n" );
document.write( " 16(2(w*h))<BR>\n" );
document.write( " 32wh is the cost of the shorter sides<BR>\n" );
document.write( "cost of the sides: <BR>\n" );
document.write( " 64wh + 32wh = 96wh the total cost of the sides<BR>\n" );
document.write( "find the cost of the materials for the cheapest such aquarium.<BR>\n" );
document.write( " 40w^2 + 96wh = total cost<BR>\n" );
document.write( "replace h with 20/w^2<BR>\n" );
document.write( " 40w^2 + 96w(20/w^2) <BR>\n" );
document.write( "multiply, cancel w<BR>\n" );
document.write( " 40w^2 + 1920/w = total cost<BR>\n" );
document.write( "we can simplify to solve, divide by 40<BR>\n" );
document.write( " w^2 + 48/w<BR>\n" );
document.write( "find the minimum on your graphing calc, w=3 is minimum cost<BR>\n" );
document.write( "then L = 6 is the length and h = 20/3^2 = 2.22 meters<BR>\n" );
document.write( "Check: 6 * 3 * 2.22 = 40 cubic meters<BR>\n" );
document.write( ":<BR>\n" );
document.write( "find the cost of the materials for the cheapest such aquarium.<BR>\n" );
document.write( "Base cost: 40*3^2 = 360<BR>\n" );
document.write( "Long sides 64*3*2.22 = 426.24<BR>\n" );
document.write( "Short sides 32*3*2.22 = 213.12<BR>\n" );
document.write( "----------------------------------<BR>\n" );
document.write( "total cost of aquarium 999.36 ~ $1000<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check using total equation<BR>\n" );
document.write( "40(3^2) + 1920/3 = 1000 <BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );