document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1054898>Question 1054898</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A student club on a college campus charges annual membership dues of P800.00, less P5.00 for each member over 50.  \r<BR>\n" );
document.write( "\n" );
document.write( "a.How many members would give the club the most revenue for annual dues?<BR>\n" );
document.write( "b.If the club considers only the number of students (bigger than 50) that will maximize the revenue, what is the amount of the maximum revenue that will be realized by the club?   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #670105 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=670105\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  A student club on a college campus charges annual membership dues of P800.00, less P5.00 for each member over 50.<BR>\n" );
document.write( "a.How many members would give the club the most revenue for annual dues?<BR>\n" );
document.write( "let x = no. of students over 50<BR>\n" );
document.write( "total revenue = r(x)<BR>\n" );
document.write( "r(x) = (50+x)(800-5x)<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "r(x) = 40000 - 250x + 800x - 5x^2<BR>\n" );
document.write( "A quadratic equation,<BR>\n" );
document.write( "-5x^2 + 550x + 40000 = 0<BR>\n" );
document.write( "max rev occurs on the axis of symmetry, x = -b/(2a) where a=-5; b=550<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-550%29%2F%282%2A-5%29 ALIGN=MIDDLE  ALT=\"%28-550%29%2F%282%2A-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = +55<BR>\n" );
document.write( "50 + 55 = 105 students would give max revenue<BR>\n" );
document.write( ":<BR>\n" );
document.write( "b.If the club considers only the number of students (bigger than 50) that will maximize the revenue, what is the amount of the maximum revenue that will be realized by the club?<BR>\n" );
document.write( "Find the cost for each student if 55 more the 50 join<BR>\n" );
document.write( "800-(55*5) = $535<BR>\n" );
document.write( "Find the revenue if 105 students pay this amt<BR>\n" );
document.write( "105 *525 = $55,125  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );