document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=863807>Question 863807</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A parcel delivery service has contracted you to design an open box with square base of length x cm and height y cm and a volume of 3600 cubic cm. Find the total surface area in terms of x and y. Also determine the dimensions for minimum surface area. (Round your answers correct to two decimal places if needed.) I know the formula to solve this is S=x^2+4xy but I don't know where to start. Can someone break this down step by step so I can understand. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #520641 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=520641\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are two equations to consider<BR>\n" );
document.write( "S = x^2 + 4xy<BR>\n" );
document.write( "V = x^2*y and V = 3600<BR>\n" );
document.write( "y = V/x^2<BR>\n" );
document.write( "S = (x^2 +4xy)<BR>\n" );
document.write( "S = (x^2 +4*x*V/x^2)<BR>\n" );
document.write( "dS/dx = 2x -4V/x^2<BR>\n" );
document.write( "now set derivative to 0 for min surface area<BR>\n" );
document.write( "2x = 4V/x^2<BR>\n" );
document.write( "x^3 = 2V<BR>\n" );
document.write( "x = (2V)^(1/3) = (7200)^1/3 = 19.31 cm<BR>\n" );
document.write( "y = 3600 / x^2 = 3600 / 19.31^2 = 9.65 cm\r<BR>\n" );
document.write( "\n" );
document.write( "   </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );