document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1042613>Question 1042613</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the profit for a veggie dog vendor is given by this function: p(v)=-.004v^2+1.32v+200, where v is the number of veggie dogs sold per day. how many veggie dogs does she need tto sell in a day to make a maximum profit </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #657596 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=657596\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When the form of the equation is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+ ALIGN=MIDDLE  ALT=\"+f%28x%29+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then the<BR>\n" );
document.write( "formula for the x-value of the vertex<BR>\n" );
document.write( "( a peak in this case ) 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( "----------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p%28v%29+=+-.004v%5E2+%2B+1.32v+%2B+200+ ALIGN=MIDDLE  ALT=\"+p%28v%29+=+-.004v%5E2+%2B+1.32v+%2B+200+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+-.004+ ALIGN=MIDDLE  ALT=\"+a+=+-.004+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+1.32+ ALIGN=MIDDLE  ALT=\"+b+=+1.32+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+v%5Bmax%5D+=+-1.32+%2F+%28+2%2A%28-.004+%29%29+ ALIGN=MIDDLE  ALT=\"+v%5Bmax%5D+=+-1.32+%2F+%28+2%2A%28-.004+%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=+v%5Bmax%5D+=+1.32%2F.008+ ALIGN=MIDDLE  ALT=\"+v%5Bmax%5D+=+1.32%2F.008+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+v%5Bmax%5D+=+165+ ALIGN=MIDDLE  ALT=\"+v%5Bmax%5D+=+165+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "She needs to sell 165 hot dogs/day to<BR>\n" );
document.write( "maximize profit<BR>\n" );
document.write( "------------------------------------<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "Plug this value back into the equation to<BR>\n" );
document.write( "get the maximum profit, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p%28v%29%5Bmax%5D+ ALIGN=MIDDLE  ALT=\"+p%28v%29%5Bmax%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p%28v%29%5Bmax%5D+=+-.004%2A165%5E2+%2B+1.32%2A165+%2B+200+ ALIGN=MIDDLE  ALT=\"+p%28v%29%5Bmax%5D+=+-.004%2A165%5E2+%2B+1.32%2A165+%2B+200+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p%28v%29%5Bmax%5D+=+-.004%2A27225+%2B+1.32%2A165+%2B+200+ ALIGN=MIDDLE  ALT=\"+p%28v%29%5Bmax%5D+=+-.004%2A27225+%2B+1.32%2A165+%2B+200+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p%28v%29%5Bmax%5D+=+-108.9+%2B+217.8+%2B+200+ ALIGN=MIDDLE  ALT=\"+p%28v%29%5Bmax%5D+=+-108.9+%2B+217.8+%2B+200+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p%28v%29%5Bmax%5D+=+108.9+%2B+200+ ALIGN=MIDDLE  ALT=\"+p%28v%29%5Bmax%5D+=+108.9+%2B+200+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p%28v%29%5Bmax%5D+=+308.9+ ALIGN=MIDDLE  ALT=\"+p%28v%29%5Bmax%5D+=+308.9+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------------<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+600%2C+400%2C+-60%2C+500%2C+-30%2C+350%2C+-.004x%5E2+%2B+1.32x+%2B+200+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+400%2C+-60%2C+500%2C+-30%2C+350%2C+-.004x%5E2+%2B+1.32x+%2B+200+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );