document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=810255>Question 810255</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An average of 100,000 people visit Riverside Park each day in the summer. The park charges $21.00 for admission. Consultants predict that for each $1.00 increase in the entrance price, the park would lose an average of 3,500 customers a day<BR>\n" );
document.write( "A)  Express the daily revenue from ticket sales, R as a function of the number of $100 price increases, x.  <BR>\n" );
document.write( "       R=f(x)=\r<BR>\n" );
document.write( "\n" );
document.write( "B)    What ticket price maximizes the revenue from ticket sales? (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 #488177 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=488177\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  An average of 100,000 people visit Riverside Park each day in the summer.<BR>\n" );
document.write( " The park charges $21.00 for admission.<BR>\n" );
document.write( " Consultants predict that for each $1.00 increase in the entrance price, the park would lose an average of 3,500 customers a day<BR>\n" );
document.write( ":<BR>\n" );
document.write( "A) Express the daily revenue from ticket sales, R as a function of the number of $1.00 price increases, x.<BR>\n" );
document.write( "R=f(x)= (100000-3500x)(21 + x)<BR>\n" );
document.write( "FOIL <BR>\n" );
document.write( "f(x) = 2100000 + 100000x - 73500x - 3500x^2<BR>\n" );
document.write( "f(x) = 2100000 + 26500x - 3500x^2<BR>\n" );
document.write( "usually written<BR>\n" );
document.write( "f(x) = -3500x^2 + 26500x + 2100000<BR>\n" );
document.write( ":<BR>\n" );
document.write( "B)   What ticket price maximizes the revenue from ticket sales? (round to the nearest cent)<BR>\n" );
document.write( "Simplify equation, divide by 500<BR>\n" );
document.write( "f(x) = -7x^2 + 53x + 4200<BR>\n" );
document.write( "Maximum occurs at the axis of symmetry which is: x = -b/(2a)<BR>\n" );
document.write( "x =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-53%29%2F%282%2A-7%29 ALIGN=MIDDLE  ALT=\"%28-53%29%2F%282%2A-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = +3.79 * $1 = $3.79 increase<BR>\n" );
document.write( "A price of $24.79 would give max revenue </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );