document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=933553>Question 933553</A>: <I><SPAN STYLE=\"word-break: break-all;\"> SOLVE FULLY. DEFINE VARIABLES, CREATE QUADRATIC EQUATION AND ANSWER PROBLEM.<BR>\n" );
document.write( "Tickets to a dance cost $4 and the projected attendance is 300 people. For every $0.10 increase in ticket price, the school dance committee predicts attendance will decrease by 5 people. Determine price of ticket that produces 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 #566982 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=566982\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Tickets to a dance cost $4 and the projected attendance is 300 people.<BR>\n" );
document.write( " For every $0.10 increase in ticket price, the school dance committee predicts attendance will decrease by 5 people.<BR>\n" );
document.write( " Determine price of ticket that produces greatest revenue.<BR>\n" );
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document.write( "Let x = the no. of 10 cent increases<BR>\n" );
document.write( "Also<BR>\n" );
document.write( "Let x = no. of 5 people reductions with each price increase<BR>\n" );
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document.write( "y = revenue for ticket sales<BR>\n" );
document.write( "y = (4+.10x)(300-5x)<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "y = 1200 - 20x + 30x - .5x^2<BR>\n" );
document.write( "A quadratic equation<BR>\n" );
document.write( "y = -.5x^2 + 10x + 1200<BR>\n" );
document.write( "greatest y (revenue) occurs 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=%28-10%29%2F%282%2A-.5%29 ALIGN=MIDDLE  ALT=\"%28-10%29%2F%282%2A-.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = +10 price increases for max revenue<BR>\n" );
document.write( "therefore the price will be:<BR>\n" );
document.write( "4 + 10(.10) = $5 is the price for max revenue <BR>\n" );
document.write( ":<BR>\n" );
document.write( "No. of tickets then (300 - 10(5)) = 250 people<BR>\n" );
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document.write( "Max revenue: 250 * 5 = $1250<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );