document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=426063>Question 426063</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the number of units x that produces a maximum revenue R in the given equation.<BR>\n" );
document.write( "R = 36x^2/3 – 2x  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #296487 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=296487\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We have the function R = 36x^(2/3) – 2x<BR>\n" );
document.write( "The function is maximized at the point where the derivative is equal to 0.<BR>\n" );
document.write( "dR/dx = 0 = (2/3)36x^(-1/3) - 2.<BR>\n" );
document.write( "Solving for x we get<BR>\n" );
document.write( "12x^(-1/3) = 1 -> x^(1/3) = 12 -> x = 12^3 = 1728<BR>\n" );
document.write( "So the answer is 1728 units.<BR>\n" );
document.write( "The graph looks like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-200%2C2000%2C-200%2C2000%2C36x%5E%282%2F3%29-2x%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-200%2C2000%2C-200%2C2000%2C36x%5E%282%2F3%29-2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );