document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1120665>Question 1120665</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An airline flies between 2 major cities daily. It normally transports 81 people a day at a cost of $210 per person. The airline estimates that it will lose 2 passengers for every $6 that it increases the fare. What should the airline charge to gain the maximum income?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #736340 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=736340\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It would be easier to use 1 passenger for every $3 raise.<BR>\n" );
document.write( "x=number of passengers changing<BR>\n" );
document.write( "(81-x)(210+3x)=17010+243x-210x-3x^2<BR>\n" );
document.write( "This is -3x^2+33x+17010<BR>\n" );
document.write( "x-value for maximum is at x=-b/2a or -33/6 or -5.50<BR>\n" );
document.write( "This makes x 75.5, with a fare of $226.50, but we need integer number of passengers. Because this is not linear, we need to look at both sides of the decimal, at 75 and 76.<BR>\n" );
document.write( "76 passengers is the optimal number at a fare of $225 each.\r<BR>\n" );
document.write( "\n" );
document.write( "81---210<BR>\n" );
document.write( "80---213<BR>\n" );
document.write( "79---216<BR>\n" );
document.write( "78---219<BR>\n" );
document.write( "77---222=17094<BR>\n" );
document.write( "76---225=17100<BR>\n" );
document.write( "75---224=16800<BR>\n" );
document.write( " </SPAN>\n" );
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