document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=888785>Question 888785</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A movie theatre can accommodate a maximum of 450 moviegoers per day. The theatre operators have determined that the profit per day, P, is related to the ticket price t, by P= -30t^2 + 450t -790 .\r<BR>\n" );
document.write( "\n" );
document.write( "a) what ticket price will maximize the daily profit?\r<BR>\n" );
document.write( "\n" );
document.write( "b) what ticket price will allow them to break-even (profit will be zero)?\r<BR>\n" );
document.write( "\n" );
document.write( "For a) I completed the square and converted the quadratic equation in to vertex form because ''k'' will represent the maximum daily profit. I got 7.5 as an answer. I am unsure whether it is correct.\r<BR>\n" );
document.write( "\n" );
document.write( "for b I calculated the x intercepts using the quadratic formula and got 2.03 and 12.97. I am not sure whether this is correct either.\r<BR>\n" );
document.write( "\n" );
document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #537693 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=537693\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A movie theatre can accommodate a maximum of 450 moviegoers per day. The theatre operators have determined that the profit per day, P, is related to the ticket price t, by P= -30t^2 + 450t -790 . <BR>\n" );
document.write( "a) what ticket price will maximize the daily profit? <BR>\n" );
document.write( "b) what ticket price will allow them to break-even (profit will be zero)? <BR>\n" );
document.write( "***<BR>\n" );
document.write( "P= -30t^2 + 450t -790<BR>\n" );
document.write( "P=-30(t^2-15t+7.5^2)+30*7.5^2-790<BR>\n" );
document.write( "P=-30(t-7.5)^2+897.5<BR>\n" );
document.write( "This is an equation of a parabola that opens down wit vertex at (7.5,897.5)<BR>\n" );
document.write( "a) what ticket price will maximize the daily profit? $7.50<BR>\n" );
document.write( "..<BR>\n" );
document.write( "0= -30t^2 + 450t -790<BR>\n" );
document.write( " -30t^2 + 450t -790=0<BR>\n" );
document.write( "-3t+45t-79=0<BR>\n" );
document.write( "solve for t by quadratic formula:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a=-3, b=45, c=-79<BR>\n" );
document.write( "ans:<BR>\n" );
document.write( "t=12.97<BR>\n" );
document.write( "or<BR>\n" );
document.write( "t=2.03<BR>\n" );
document.write( "b) what ticket price will allow them to break-even (profit will be zero)? $2.03 and $12.97<BR>\n" );
document.write( "congratulations! you got the same answers I got </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );