document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1003563>Question 1003563</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A small cruising ship that can hold up to 64 people provides three-day excursions to groups of 40 or more.  If the group contains 40 people, each person pays $76.  The cost per person for all members of the party is reduced by $1 for each person in excess of 40.  Find the size of the group that maximizes income for the owners of the ship.   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #620244 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=620244\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x, number of persons<BR>\n" );
document.write( "Price is  76 dollars person initially.\r<BR>\n" );
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document.write( "Subtract 1 dollar for each person more than 40 persons.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=76-x ALIGN=MIDDLE  ALT=\"76-x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, price for x added persons.<BR>\n" );
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document.write( "Group cost, meaning revenue for the cruise ship company:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%2876-x%29%2840%2Bx%29%29 ALIGN=MIDDLE  ALT=\"highlight%28%2876-x%29%2840%2Bx%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Treat this as a revenue function, y for convenience.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=%2876-x%29%28x%2B40%29%29 ALIGN=MIDDLE  ALT=\"highlight%28y=%2876-x%29%28x%2B40%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is factored.  Find the maximum value.  It will  happen exactly in the middle between the two roots of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2876-x%29%28x%2B40%29=0 ALIGN=MIDDLE  ALT=\"%2876-x%29%28x%2B40%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Zeros are at 76 and -40.  The independent value in the middle is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2876%2B%28-40%29%29%2F2=18 ALIGN=MIDDLE  ALT=\"%2876%2B%28-40%29%29%2F2=18\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "MAXIMUM REVENUE:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%2876-18%29%2818%2B40%29=3364 ALIGN=MIDDLE  ALT=\"y=%2876-18%29%2818%2B40%29=3364\"   DISABLED_style= \"max-width:90%; height:auto;\" > dollars.<BR>\n" );
document.write( "NUMBER OF PEOPLE FOR THIS MAX IS  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=18%29 ALIGN=MIDDLE  ALT=\"highlight%28x=18%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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