document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=389250>Question 389250</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Each year a school’s booster club holds a dance to raise funds. In the past, the profit the club makes after paying for the bank and other costs has been modeled by the function P(t)= -16t² + 800t – 4000, where t represents the ticket price in dollars. <BR>\n" );
document.write( "a.	What ticket price gives the maximum profit?<BR>\n" );
document.write( "b.	What is the maximum profit?<BR>\n" );
document.write( "c.	What ticket price(s) would generate a profit of $5424? <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #275786 by </B><A HREF=/tutors/aboutme.mpl?userid=CharlesG2><B>CharlesG2(834)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CharlesG2><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=275786\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Each year a school’s booster club holds a dance to raise funds. In the past, the profit the club makes after paying for the bank and other costs has been modeled by the function P(t)= -16t² + 800t – 4000, where t represents the ticket price in dollars. <BR>\n" );
document.write( "a.	What ticket price gives the maximum profit?<BR>\n" );
document.write( "b.	What is the maximum profit?<BR>\n" );
document.write( "c.	What ticket price(s) would generate a profit of $5424? \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "P(t) = -16t^2 + 800t - 4000<BR>\n" );
document.write( "standard form parabola is y = ax^2 + bx + c,<BR>\n" );
document.write( "here a = -16, b = 800, c = -4000,<BR>\n" );
document.write( "vertex x-coordinate = -b/2a = -800/(2 * -16) = -800/-32 = 25<BR>\n" );
document.write( "P(25) = -16 * 25^2 + 800 * 25 - 4000<BR>\n" );
document.write( "P(25) = -16 * 625 + 20000 - 4000<BR>\n" );
document.write( "P(25) = -10000 + 20000 - 4000<BR>\n" );
document.write( "P(25) = 10000 - 4000 = 6000<BR>\n" );
document.write( "$25 dollar ticket price gives maximum profit of $6000<BR>\n" );
document.write( "for $5424 profit:<BR>\n" );
document.write( "5424 = -16t^2 + 800t - 4000<BR>\n" );
document.write( "0 = -16t^2 + 800t - 9424<BR>\n" );
document.write( "0 = t^2 - 50t + 589<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%2850+%2B-+sqrt%28+%28-50%29%5E2+-+4%2A589+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"t+=+%2850+%2B-+sqrt%28+%28-50%29%5E2+-+4%2A589+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%2850+%2B-+sqrt%28+2500+-+2356+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"t+=+%2850+%2B-+sqrt%28+2500+-+2356+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%2850+%2B-+sqrt%28+144+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"t+=+%2850+%2B-+sqrt%28+144+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%2850+%2B-+12%29%2F2+ ALIGN=MIDDLE  ALT=\"t+=+%2850+%2B-+12%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = 62/2 or t = 38/2<BR>\n" );
document.write( "t = 31 or t = 19<BR>\n" );
document.write( "either $19 or $31 dollar ticket prices\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );