document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=82907>Question 82907</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The monthly profit, P, in thousands of dollars, of a bicycle company can be estimated by the formula P=-2x(squared)+16X-12......where X is the number of bicycles, in hundreds, sold per month.<BR>\n" );
document.write( "a) How many bicycles must be sold for maximum profit?<BR>\n" );
document.write( "b) What is the minimum number of bicycles that must be sold to break even?<BR>\n" );
document.write( "c) What is the maximum number of bicycles that must be sold to break even? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #59507 by </B><A HREF=/tutors/aboutme.mpl?userid=Nate><B>Nate(3500)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Nate><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=59507\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+=+-2x%5E2+%2B+16x+-+12 ALIGN=MIDDLE  ALT=\"P+=+-2x%5E2+%2B+16x+-+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a) How many bicycles must be sold for maximum profit?<BR>\n" );
document.write( "This is a vertical parabola that is opening downward. The vertex will be the maximum point for P.<BR>\n" );
document.write( "v(-b/(2a),f(x))<BR>\n" );
document.write( "v(-16/(-4),f(x))<BR>\n" );
document.write( "v(4,f(4))<BR>\n" );
document.write( "v(4,20) or $20,000 dollars<BR>\n" );
document.write( "b) What is the minimum number of bicycles that must be sold to break even?<BR>\n" );
document.write( "c) What is the maximum number of bicycles that must be sold to break even?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+-2x%5E2+%2B+16x+-+12 ALIGN=MIDDLE  ALT=\"0+=+-2x%5E2+%2B+16x+-+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+x%5E2+-+8x+%2B+6 ALIGN=MIDDLE  ALT=\"0+=+x%5E2+-+8x+%2B+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6+=+x%5E2+-+8x ALIGN=MIDDLE  ALT=\"-6+=+x%5E2+-+8x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Quadratic Formula or Solving Squares<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10+=+%28x+-+4%29%5E2 ALIGN=MIDDLE  ALT=\"10+=+%28x+-+4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+%2B-+sqrt%2810%29+=+x ALIGN=MIDDLE  ALT=\"4+%2B-+sqrt%2810%29+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Min: 4 - sqrt(10) = 0.8377.... or about 1 which is 100 bikes<BR>\n" );
document.write( "Max: 4 + sqrt(10) = 7.1622.... or about 7 which is 700 bikes<BR>\n" );
document.write( "~ Proof ~<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-2%2C12%2C-2%2C20%2C-2x%5E2+%2B+16x+-+12%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-2%2C12%2C-2%2C20%2C-2x%5E2+%2B+16x+-+12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );