document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=62157>Question 62157</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A dreaded word problem.  I can't figure this one out. \r<BR>\n" );
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document.write( "The Municipal transit serves 150,000 commuters daily when the fair is $1.80.<BR>\n" );
document.write( "Market research has determined that every penny decrease in the fare will result in 1,000 new riders.  What fare will maxmize revenue?  \r<BR>\n" );
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document.write( "Any help would be appreciated.  Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #42912 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=42912\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The Municipal transit serves 150,000 commuters daily when the fair is $1.80.<BR>\n" );
document.write( "Market research has determined that every penny decrease in the fare will result in 1,000 new riders. What fare will maxmize revenue? <BR>\n" );
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document.write( "Look at it a penny at a time and try to see the pattern:<BR>\n" );
document.write( "If Fare is 180 cents the # of commuters is 150,000<BR>\n" );
document.write( "If Fare is 180-1 cents the # of commuters is 150,000+1000<BR>\n" );
document.write( "If Fare is 180-2 cents the # of commuters is 150,000+2(1000)<BR>\n" );
document.write( "...<BR>\n" );
document.write( "If Fare is 180-x cents the # of commuters is 150,000+x(1000)<BR>\n" );
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document.write( "EQUATION:<BR>\n" );
document.write( "Revenue = (Fare)(# of commuters)<BR>\n" );
document.write( "R(x)=(180-x)(150,000+1000x)<BR>\n" );
document.write( "R(x)= -1000x^2-150000x+180000x+180*150000<BR>\n" );
document.write( "R(x)=-1000x^2+30000x+180*150000<BR>\n" );
document.write( "Maximum occurs at x=-b/2a = -30000/-2000=15<BR>\n" );
document.write( "Maximum Revenue comes when Fare = 180-15=165 cent or $1.65<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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