document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=969591>Question 969591</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A harbor ferry service has about 240 000 riders per day for a fare of $2. The port authority wants to increase the fare to help with increasing operational costs. Research has shown that for every $0.10 increase in the fare the number of riders will drop by 10 000.\r<BR>\n" );
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document.write( "a)What increase in the fare will maximize the revenue?<BR>\n" );
document.write( "b) what is the new fare?<BR>\n" );
document.write( "c) what is the revenue that will be received from the new fare?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #592475 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=592475\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A harbor ferry service has about 240 000 riders per day for a fare of $2.<BR>\n" );
document.write( " The port authority wants to increase the fare to help with increasing operational costs.<BR>\n" );
document.write( " Research has shown that for every $0.10 increase in the fare the number of riders will drop by 10 000.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "a)What increase in the fare will maximize the revenue?<BR>\n" );
document.write( "let x = no. of 10 cent increases and also = no. 10000 rider decreases<BR>\n" );
document.write( "Revenue = riders * fare<BR>\n" );
document.write( "r(x) = (240000 - 10000x)(2 + .10x)<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "r(x) = 480000 + 24000x - 20000x - 1000x^2<BR>\n" );
document.write( "r(x) = -1000x^2 + 4000x + 480000<BR>\n" );
document.write( "simplify, divide by 1000<BR>\n" );
document.write( "r(x) = -x^2 + 4x + 480<BR>\n" );
document.write( "The axis of symmetry will give us max revenue; x = -b/2a<BR>\n" );
document.write( "x = -4/(2*-1)<BR>\n" );
document.write( "x = 2 fare increases of $.10<BR>\n" );
document.write( ":<BR>\n" );
document.write( "b) what is the new fare?<BR>\n" );
document.write( "2 + 2(.10) = $2.20 is the new fare<BR>\n" );
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document.write( "c) what is the revenue that will be received from the new fare?<BR>\n" );
document.write( "(240000 - 2(10000)) * $2.20 = $484,000  </SPAN>\n" );
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