document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1030225>Question 1030225</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose you own a party bus and you book groups of 20 to 70 people for a day trip.  The cost per person is $30 minus 25 cents for every ticket sold.  If gas and other costs are $200, how many tickets should you sell to maximize your profit?   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #645153 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=645153\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x = # of tickets sold.<BR>\n" );
document.write( "==> Total revenues  = x(30 - 0.25x) and Total costs = 200\r<BR>\n" );
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document.write( "==> Total profits = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2830+-+0.25x%29+-+200+=+-0.25x%5E2+%2B+30x+-200 ALIGN=MIDDLE  ALT=\"x%2830+-+0.25x%29+-+200+=+-0.25x%5E2+%2B+30x+-200\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Taking the derivative and equating to 0 to get the extreme value, \r<BR>\n" );
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document.write( "-0.5x + 30 = 0<BR>\n" );
document.write( "==> x = 30/0.5 = 60\r<BR>\n" );
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document.write( "(The 2nd derivative p\" = -0.5 < 0, hence we are assured an absolute maximum.)\r<BR>\n" );
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document.write( "Therefore, he has to sell 60 tickets to maximize profits. </SPAN>\n" );
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