document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1113217>Question 1113217</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A printed page has 1-inch at the top and bottom, and 3/4-inch margins on each side. The area of the printed portion of the pages is 48 square inches. Find the dimension of the page, which has the smallest possible area. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #728212 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=728212\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x is width, y is length of printed area<BR>\n" );
document.write( "xy=48<BR>\n" );
document.write( "the whole page is x+1.5 inches and y+2 inches<BR>\n" );
document.write( "xy+2x+1.5y+3 has to be minimized.  xy=48<BR>\n" );
document.write( "2x+1.5(48/x)+51 has to be minimized<BR>\n" );
document.write( "2x+(72/x)+51<BR>\n" );
document.write( "Take the derivative and set equal to 0.<BR>\n" );
document.write( "2-(72/x^2)=0<BR>\n" );
document.write( "72=2x^2<BR>\n" );
document.write( "x^2=36<BR>\n" );
document.write( "x=6 inches<BR>\n" );
document.write( "y=8 inches<BR>\n" );
document.write( "second derivative is +144/x^3, which is positive, so the critical point is a minimum.<BR>\n" );
document.write( "The page has dimensions of 7.5 x 10 or 75 in^2, </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );