document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1031134>Question 1031134</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The tickets to a charity concert will sell out if the price is $15 per ticket. It is estimated that for each $1 increase in ticket's price, 20 tickets will remain unsold. What ticket price will maximize the charity's profit, if there are total 500 seats in the concert hall? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #645862 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=645862\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> With zero increase in ticket price, The <BR>\n" );
document.write( "number of tickets sold is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n+=+500+ ALIGN=MIDDLE  ALT=\"+n+=+500+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and income is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+15%2A500+=+7500+ ALIGN=MIDDLE  ALT=\"+15%2A500+=+7500+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "When there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2An+ ALIGN=MIDDLE  ALT=\"+1%2An+\"   DISABLED_style= \"max-width:90%; height:auto;\" > dollar increases<BR>\n" );
document.write( "in the ticket price, the income is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+I+=+%28+15+%2B+n+%29%2A%28+500+-+20n+%29+ ALIGN=MIDDLE  ALT=\"+I+=+%28+15+%2B+n+%29%2A%28+500+-+20n+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+I+=+7500+%2B+500n+-+300n+-+20n%5E2+ ALIGN=MIDDLE  ALT=\"+I+=+7500+%2B+500n+-+300n+-+20n%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+I+=+-20n%5E2+%2B+200n+%2B+7500+ ALIGN=MIDDLE  ALT=\"+I+=+-20n%5E2+%2B+200n+%2B+7500+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This function is a maximum when:<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+=+-20+ ALIGN=MIDDLE  ALT=\"+a+=+-20+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+200+ ALIGN=MIDDLE  ALT=\"+b+=+200+\"   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+=+-200+%2F+%28+2%2A%28-20%29+%29+ ALIGN=MIDDLE  ALT=\"+n%5Bmax%5D+=+-200+%2F+%28+2%2A%28-20%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+=+5+ ALIGN=MIDDLE  ALT=\"+n%5Bmax%5D+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+I+=+-20%2A5%5E2+%2B+200%2A5+%2B+7500+ ALIGN=MIDDLE  ALT=\"+I+=+-20%2A5%5E2+%2B+200%2A5+%2B+7500+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+I+=+-500+%2B+1000+%2B+7500+ ALIGN=MIDDLE  ALT=\"+I+=+-500+%2B+1000+%2B+7500+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+I+=+8000+ ALIGN=MIDDLE  ALT=\"+I+=+8000+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "With <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n+=+5+ ALIGN=MIDDLE  ALT=\"+n+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" > $1 increases in ticket price,<BR>\n" );
document.write( "the price that will maximize profit is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+15+%2B+n+=+15+%2B+5+ ALIGN=MIDDLE  ALT=\"+15+%2B+n+=+15+%2B+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+15+%2B+n+=+20+ ALIGN=MIDDLE  ALT=\"+15+%2B+n+=+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "$20<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "Here's the plot of income:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-10%2C+30%2C+-1000%2C+9000%2C+-20x%5E2+%2B+200x+%2B+7500+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-10%2C+30%2C+-1000%2C+9000%2C+-20x%5E2+%2B+200x+%2B+7500+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );