document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=337535>Question 337535</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A new movies theater after several months of incrementing finds that for every 20 c increase in ticket price the number of tickets for each showing decrease by 10. Similarly for every 20 c decrease in price showings increase by 10. On average the theater sells 500 tickets at $ 8 each. \r<BR>\n" );
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document.write( "how much should they charge for a ticket to maximize the revenue.?<BR>\n" );
document.write( "Also explain how ticket price is related to total revenue?\r<BR>\n" );
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document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #242111 by </B><A HREF=/tutors/aboutme.mpl?userid=nyc_function><B>nyc_function(2741)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nyc_function><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=nyc_function><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=242111\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Revenue = f ( Ticket Price, Tickets Sold ) = Price*Sold \r<BR>\n" );
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document.write( "Tickets Sold = f ( Price ) = m*Price + b<BR>\n" );
document.write( "Sold = -10/(0.2)*(Price) +b <BR>\n" );
document.write( "500 = -10/(0.2)*(8) + b<BR>\n" );
document.write( "900 = b<BR>\n" );
document.write( "Ticket Sold = -10/(0.2)*Price + 900<BR>\n" );
document.write( "Tickets Sold = -50*Price + 900\r<BR>\n" );
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document.write( "Revenue = Price * Sold = Price * (-50*Price + 900)<BR>\n" );
document.write( "Revenue = -50*Price^2 + 900*Price\r<BR>\n" );
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document.write( "Take the derivative and set to 0:<BR>\n" );
document.write( "dRev = -100*Price + 900<BR>\n" );
document.write( "0 = -100*Price+900<BR>\n" );
document.write( "Price = 9.00\r<BR>\n" );
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document.write( "This is a maximum because the second derivative is negative:<BR>\n" );
document.write( "d^2Rev = -100<BR>\n" );
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