document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1085633>Question 1085633</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A fundraising company charges $200 plate for a local charity and sells 300 tickets. For every $10 increase they will lose 5 ticket sales. What would they charge to make a maximum profit and what is the profit? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #699721 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=699721\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n+ ALIGN=MIDDLE  ALT=\"+n+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the number of $10 <BR>\n" );
document.write( "increases in the ticket price<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+ ALIGN=MIDDLE  ALT=\"+P+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the profit<BR>\n" );
document.write( "------------------------------<BR>\n" );
document.write( "[ profit ] = [ tickets sold ] x [ income from selling 1 ticket ]<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+%28+300+-+5n+%29%2A%28+200+%2B+10n+%29+ ALIGN=MIDDLE  ALT=\"+P+=+%28+300+-+5n+%29%2A%28+200+%2B+10n+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+60000+-+1000n+%2B+3000n+-+50n%5E2+ ALIGN=MIDDLE  ALT=\"+P+=+60000+-+1000n+%2B+3000n+-+50n%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+-50n%5E2+%2B+2000n+%2B+60000+ ALIGN=MIDDLE  ALT=\"+P+=+-50n%5E2+%2B+2000n+%2B+60000+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+-n%5E2+%2B+40n+%2B+1200+ ALIGN=MIDDLE  ALT=\"+P+=+-n%5E2+%2B+40n+%2B+1200+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "This is a parabola with a maximum. Use the formula for<BR>\n" );
document.write( "the ( n, P ) of the vertex ( maximum in this case )<BR>\n" );
document.write( "---------------------------------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n%5Bmax%5D+=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+n%5Bmax%5D+=+-b%2F%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > where<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+-1+ ALIGN=MIDDLE  ALT=\"+a+=+-1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+40+ ALIGN=MIDDLE  ALT=\"+b+=+40+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n%5Bmax%5D+=+-40%2F%282%2A%28-1%29%29+ ALIGN=MIDDLE  ALT=\"+n%5Bmax%5D+=+-40%2F%282%2A%28-1%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n%5Bmax%5D+=+20+ ALIGN=MIDDLE  ALT=\"+n%5Bmax%5D+=+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, for a maximum profit, they would charge:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+200+%2B+10n+=+200+%2B+10%2A20+ ALIGN=MIDDLE  ALT=\"+200+%2B+10n+=+200+%2B+10%2A20+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+200+%2B+10n+=+400+ ALIGN=MIDDLE  ALT=\"+200+%2B+10n+=+400+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "$400 / plate<BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "To find the profit, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+ ALIGN=MIDDLE  ALT=\"+P+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, plug the value for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n+ ALIGN=MIDDLE  ALT=\"+n+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "back into the equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+-n%5E2+%2B+40n+%2B+1200+ ALIGN=MIDDLE  ALT=\"+P+=+-n%5E2+%2B+40n+%2B+1200+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P%5Bmax%5D+=+-20%5E2+%2B+40%2A20+%2B+1200+ ALIGN=MIDDLE  ALT=\"+P%5Bmax%5D+=+-20%5E2+%2B+40%2A20+%2B+1200+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P%5Bmax%5D+=+-400+%2B+800+%2B+1200+ ALIGN=MIDDLE  ALT=\"+P%5Bmax%5D+=+-400+%2B+800+%2B+1200+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P%5Bmax%5D+=+1600+ ALIGN=MIDDLE  ALT=\"+P%5Bmax%5D+=+1600+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The maximum profit is $1600<BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( "Feel free to get a 2nd opinion if needed<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );