document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=529847>Question 529847</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 5. Find the maximum profit and the number of units that must be produced and sold in<BR>\n" );
document.write( "     order to yield the maximum profit. Assume that revenue, R(x), and cost, C(x), are in<BR>\n" );
document.write( "     thousands of dollars and x in thousands of units for<BR>\n" );
document.write( "                      R(x) = 100x-x2<BR>\n" );
document.write( "                     C(x) =  1/3 x^3-6x^2+89x+100<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #349775 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=349775\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the maximum profit and the number of units that must be produced and sold in<BR>\n" );
document.write( "order to yield the maximum profit. Assume that revenue, R(x), and cost, C(x), are in<BR>\n" );
document.write( "thousands of dollars and x in thousands of units for<BR>\n" );
document.write( "R(x) = 100x-x2<BR>\n" );
document.write( "C(x) = 1/3 x^3-6x^2+89x+100\r<BR>\n" );
document.write( "\n" );
document.write( "----------<BR>\n" );
document.write( "Profit = Revenue - Cost<BR>\n" );
document.write( "---<BR>\n" );
document.write( "P(x) = 100x-x^2-[(1/3)x^3-6x^2+89x+100]<BR>\n" );
document.write( "----<BR>\n" );
document.write( "P(x) = (-1/3)x^3+5x^2+11x-100<BR>\n" );
document.write( "---<BR>\n" );
document.write( "P'(x) = -x^2+10x+11<BR>\n" );
document.write( "---<BR>\n" );
document.write( "P''(x) = -2x+10<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Solve: -x^2+10x+11 = 0<BR>\n" );
document.write( "x^2-10x-11 = 0<BR>\n" );
document.write( "(x-11)(x+1) = 0<BR>\n" );
document.write( "x = -1 or x = 11<BR>\n" );
document.write( "---<BR>\n" );
document.write( "P''(-1) = -2(-1)+10 = 12 (minimum at (-1,f(-1)))<BR>\n" );
document.write( "P''(11) = -2(11)+10 = -12 (maximum at (11,f(11))<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Graph of P(x):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-10%2C50%2C-50%2C200%2C%28-1%2F3%29x%5E3%2B5x%5E2%2B11x-100%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-10%2C50%2C-50%2C200%2C%28-1%2F3%29x%5E3%2B5x%5E2%2B11x-100%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "===========<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );