document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=980573>Question 980573</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A health club currently charges its 2,000 clients monthly membership dues of $44. The board of directors decides to increase the monthly membership dues. Market research shows that each $1 increase in dues will result in the loss of 7 clients. How much should the club charge each month to optimize the revenue from monthly dues? Round to the nearest cent. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #601751 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=601751\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A health club currently charges its 2,000 clients monthly membership dues of $44.<BR>\n" );
document.write( " The board of directors decides to increase the monthly membership dues.<BR>\n" );
document.write( " Market research shows that each $1 increase in dues will result in the loss of 7 clients.<BR>\n" );
document.write( " How much should the club charge each month to optimize the revenue from monthly dues?<BR>\n" );
document.write( " Round to the nearest cent.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "let x = no. of $1 increases in dues and no. of 7 client losses<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Write a revenue equation; Rev = monthly charge * no. of clients<BR>\n" );
document.write( "R(x) = (44 + x)*(2000-7x)<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "R(x) = 88000 - 308x + 2000x - 7x^2<BR>\n" );
document.write( "R(x) = -7x^2 + 1692x + 88000<BR>\n" );
document.write( "A quadratic equation; the max will be at the axis of symmetry x = -b/(2a)<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1692%29%2F%282%2A-7%29 ALIGN=MIDDLE  ALT=\"%28-1692%29%2F%282%2A-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1692%29%2F%28-14%29 ALIGN=MIDDLE  ALT=\"%28-1692%29%2F%28-14%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = $120.86 increase; 44 + 120.86 = $164.86 a month dues for max revenue<BR>\n" );
document.write( ":<BR>\n" );
document.write( "That seem unrealistic, but there it is. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );