document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1180633>Question 1180633</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Studies have shown that 400 people attend a high school basketball game when the admission price is $30 in the championship game, admission prices will increase for every $0.25 increase, 20 fewer people will attend. At what ticket will the revenue be maximized? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #810405 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=810405\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I think you mean 2 fewer people, not 20, because if the ticket sales are $30.25 and 380 people attend, one will be losing money, compared to 400 and $30.<BR>\n" );
document.write( "Let x is number of $0.25 increase and multiples of 2 people.<BR>\n" );
document.write( "(400-x)(($30+0.25x)<BR>\n" );
document.write( "=12000-30x+100x-5x^2<BR>\n" );
document.write( "the maximum is at x=-b/2a for this negative quadratic of -5x^2+70x+12000<BR>\n" );
document.write( "this is x=70/10=7<BR>\n" );
document.write( "so at $31.75 (7*$0.25-$1.75) and 386 people  (400-7*2)<BR>\n" );
document.write( "there is a maximum, or $12,255.50<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-5%2C10%2C-500%2C14000%2C-5x%5E2%2B70x%2B12000%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-5%2C10%2C-500%2C14000%2C-5x%5E2%2B70x%2B12000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );