document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=890205>Question 890205</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For a charter flight, an airline charges a fare of $180 per person plus $10 per person for each unsold seat on the plane. If the plane holds 100 passengers and if x represents the number of unsold seats, <BR>\n" );
document.write( "(i) find an expression for the total revenue received for the flight.				      	<BR>\n" );
document.write( "(ii) Find the maximum number of unsold seats that the plane can have   			      	<BR>\n" );
document.write( "(iii) Hence find the maximum revenue for the flight.  	                  	<BR>\n" );
document.write( "	[Hint: To find an expression for the total revenue, multiply the number of people flying, by the price per ticket.] </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #538791 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=538791\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For a charter flight, an airline charges a fare of $180 per person plus $10 per person for each unsold seat on the plane. If the plane holds 100 passengers and if x represents the number of unsold seats, <BR>\n" );
document.write( "(i) find an expression for the total revenue received for the flight.<BR>\n" );
document.write( "let x=number of unsold seats<BR>\n" );
document.write( "100-x=number of seats sold<BR>\n" );
document.write( "fare price=(180+10x)<BR>\n" );
document.write( "Revenue=	fare price*number of seats sold=(180+10x)(100-x)<BR>\n" );
document.write( "R=18000+1000x-180x-10x^2<BR>\n" );
document.write( "R=-10x^2+820x+18000=0<BR>\n" );
document.write( "R=-x^2+82x+1800<BR>\n" );
document.write( "complete the square:<BR>\n" );
document.write( "R=-(x^2-82+41^2)+41^2+1800<BR>\n" );
document.write( "R=-(x-41)^2+3481<BR>\n" );
document.write( "This is an equation of a parabola that open down with vertex at (41,3481)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "(ii) Find the maximum number of unsold seats that the plane can have<BR>\n" );
document.write( " maximum number of unsold seats that the plane can have=100<BR>\n" );
document.write( "...<BR>\n" );
document.write( "(iii) Hence find the maximum revenue for the flight. <BR>\n" );
document.write( "maximum revenue for the flight=$3,481 when 41 seats are sold </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );