document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1147418>Question 1147418</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The revenue at the Assembly Center depends on the number of seats sold for the Willie Williams and the Wranglers concert. At $10 per ticket, they will fill all 8000 seats. The manager knows that for every $1 increase in the price, 500 tickets will go unsold.  If the revenue in dollars, 𝑅(𝑝), is given by<BR>\n" );
document.write( "𝑅(𝑝) = −500𝑝^2 + 13000𝑝, where 𝑝 is the price per ticket sold.<BR>\n" );
document.write( "What ticket price will produce a maximum revenue? What is the maximum<BR>\n" );
document.write( "revenue? You must show this algebraically.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #768742 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=768742\">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=+k+ ALIGN=MIDDLE  ALT=\"+k+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the number of $1 increases in price/ticket<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%28p%29+=+p%2A%28+8000+-+500k+%29+ ALIGN=MIDDLE  ALT=\"+R%28p%29+=+p%2A%28+8000+-+500k+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-500p%5E2+%2B+13000p+=+p%2A%28+8000+-+500k+%29+ ALIGN=MIDDLE  ALT=\"+-500p%5E2+%2B+13000p+=+p%2A%28+8000+-+500k+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-500p+%2B+13000+=+8000+-+500k+ ALIGN=MIDDLE  ALT=\"+-500p+%2B+13000+=+8000+-+500k+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-500p+=+-500k+-+5000+ ALIGN=MIDDLE  ALT=\"+-500p+=+-500k+-+5000+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p+=+k+%2B+10+ ALIGN=MIDDLE  ALT=\"+p+=+k+%2B+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This shows the equation works<BR>\n" );
document.write( "--------------------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%28p%29+=+-500p%5E2+%2B+13000p+ ALIGN=MIDDLE  ALT=\"+R%28p%29+=+-500p%5E2+%2B+13000p+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The maximum is at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p+=+-b%2F2a+ ALIGN=MIDDLE  ALT=\"+p+=+-b%2F2a+\"   DISABLED_style= \"max-width:90%; height:auto;\" > when the equation has the form<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%28p%29+=+a%2Ap%5E2+%2B+b%2Ap+ ALIGN=MIDDLE  ALT=\"+R%28p%29+=+a%2Ap%5E2+%2B+b%2Ap+\"   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 ALIGN=MIDDLE  ALT=\"+p%5Bmax%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >  is at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-13000%2F%28+2%2A%28-500%29%29+ ALIGN=MIDDLE  ALT=\"+-13000%2F%28+2%2A%28-500%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=+p%5Bmax%5D+=+13+ ALIGN=MIDDLE  ALT=\"+p%5Bmax%5D+=+13+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The maximum revenue is at a ticket price of $13/ticket<BR>\n" );
document.write( "which is after three $1 increases in price/ticket <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k=3+ ALIGN=MIDDLE  ALT=\"+k=3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Here's the plot:<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-5%2C+30%2C+-10000%2C+100000%2C+-500x%5E2+%2B+13000x%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-5%2C+30%2C+-10000%2C+100000%2C+-500x%5E2+%2B+13000x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );