document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1078618>Question 1078618</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A pizza shop has determined that it can sell x pizzas per night at a price of (9 - 0.02 x) dollars per pizza. There are fixed costs totalling $110 per night to run the shop, plus $3 for each pizza made. To maximize profit, how many pizzas should be made each night?\r<BR>\n" );
document.write( "\n" );
document.write( "To achieve a maximum profit of $_______________ per night, make____________ pizzas a night. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #693076 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=693076\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The income per night is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%2A%28+-.02x+%2B+9+%29+ ALIGN=MIDDLE  ALT=\"+x%2A%28+-.02x+%2B+9+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The cost to make pizza per night is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+%2B+110+ ALIGN=MIDDLE  ALT=\"+3x+%2B+110+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------------<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;\" > = profit per night<BR>\n" );
document.write( "[ profit ] = [ income ] - [ cost ]<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+x%2A%28+-.02x+%2B+9+%29+-+3x+-+110+ ALIGN=MIDDLE  ALT=\"+P+=+x%2A%28+-.02x+%2B+9+%29+-+3x+-+110+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+-.02x%5E2+%2B+9x+-+3x+-+110+ ALIGN=MIDDLE  ALT=\"+P+=+-.02x%5E2+%2B+9x+-+3x+-+110+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+-.02x%5E2+%2B+6x+-+110+ ALIGN=MIDDLE  ALT=\"+P+=+-.02x%5E2+%2B+6x+-+110+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------------------<BR>\n" );
document.write( "The x-value of the maximum is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5Bmax%5D+=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+x%5Bmax%5D+=+-b%2F%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+-.02+ ALIGN=MIDDLE  ALT=\"+a+=+-.02+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+6+ ALIGN=MIDDLE  ALT=\"+b+=+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-b%2F%282a%29+=+-6%2F%282%2A%28-.02%29%29+ ALIGN=MIDDLE  ALT=\"+-b%2F%282a%29+=+-6%2F%282%2A%28-.02%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=+x%5Bmax%5D+=+-6%2F%28-.04%29+ ALIGN=MIDDLE  ALT=\"+x%5Bmax%5D+=+-6%2F%28-.04%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5Bmax%5D+=+150+ ALIGN=MIDDLE  ALT=\"+x%5Bmax%5D+=+150+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "plug this back into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+ ALIGN=MIDDLE  ALT=\"+P+\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P%5Bmax%5D+=+-.02%2A150%5E2+%2B+6%2A150+-+110+ ALIGN=MIDDLE  ALT=\"+P%5Bmax%5D+=+-.02%2A150%5E2+%2B+6%2A150+-+110+\"   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+=+-450+%2B+900+-+110+ ALIGN=MIDDLE  ALT=\"+P%5Bmax%5D+=+-450+%2B+900+-+110+\"   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+=+340+ ALIGN=MIDDLE  ALT=\"+P%5Bmax%5D+=+340+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "The maximum profit of $340/night can be<BR>\n" );
document.write( "earned by making 150 pizzas<BR>\n" );
document.write( "--------------------------------<BR>\n" );
document.write( "Here's a plot of the profit function:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-40%2C+350%2C+-40%2C+400%2C+-.02x%5E2+%2B+6x+-+110+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-40%2C+350%2C+-40%2C+400%2C+-.02x%5E2+%2B+6x+-+110+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );