document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1153135>Question 1153135</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Tickets to a school dance cost $4 and the projected attendance is 300 people. For every $1 increase in the ticket price, the dance committee projects that attendance will decrease by 5 attendees. Determine the dance committee’s greatest possible revenue. What ticket price will produce the<BR>\n" );
document.write( "greatest revenue?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #775292 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=775292\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Tickets to a school dance cost $4 and the projected attendance is 300 people.<BR>\n" );
document.write( " For every $1 increase in the ticket price, the dance committee projects that attendance will decrease by 5 attendees.<BR>\n" );
document.write( " Determine the dance committee’s greatest possible revenue. What ticket price will produce the greatest revenue?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let x = no. of $1 increases and no. of 5 less attendees<BR>\n" );
document.write( "Revenue = ticket price * no. of attendees<BR>\n" );
document.write( "R(x) = (4 + x) * (300 - 5x)<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "R(x) = 1200 - 20x + 300x - 5x^2<BR>\n" );
document.write( "a quadratic equation<BR>\n" );
document.write( "R(x) = -5x^2 + 280x + 1200<BR>\n" );
document.write( "Max rev occurs on the line of symmetry, using x = -b/(2a)<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-280%29%2F%282%2A-5%29 ALIGN=MIDDLE  ALT=\"%28-280%29%2F%282%2A-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 28 ea $1 increases will give max revenue<BR>\n" );
document.write( "That would be: 4 + 28 = $32 a ticket<BR>\n" );
document.write( ":<BR>\n" );
document.write( "No. attending the dance: 300 - (5*28) = 160 attendees<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Max revenue: 32 * 160 = $5120 vs only $1200 at original price<BR>\n" );
document.write( " </SPAN>\n" );
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