document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=765848>Question 765848</A>: <I><SPAN STYLE=\"word-break: break-all;\"> John owns a hot dog stand. He has found that his profit is represented by the equation P = -x2 + 56x + 77, with<BR>\n" );
document.write( "P being profit in dollars and x the number of hot dogs. Using this model, what is the maximum profit that John<BR>\n" );
document.write( "can make? How many hot dogs must he sell in order to to obtain that maximum profit?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #466451 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=466451\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+=+-x%5E2+%2B+56x+%2B+77 ALIGN=MIDDLE  ALT=\"P+=+-x%5E2+%2B+56x+%2B+77\"   DISABLED_style= \"max-width:90%; height:auto;\" >........this is a parabola; since the coefficient of leading term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, parabola turns downward and the vertex will be maximum\r<BR>\n" );
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document.write( "so, we need to find the coordinates (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" >) of a vertex\r<BR>\n" );
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document.write( "use the formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+-b%2F2a ALIGN=MIDDLE  ALT=\"h+=+-b%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > coordinate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the vertex of a parabola and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+P%28h%29 ALIGN=MIDDLE  ALT=\"k+=+P%28h%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > coordinate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the vertex\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+-56%2F2%28-1%29 ALIGN=MIDDLE  ALT=\"h+=+-56%2F2%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+-56%2F-2 ALIGN=MIDDLE  ALT=\"h+=+-56%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+28 ALIGN=MIDDLE  ALT=\"h+=+28\"   DISABLED_style= \"max-width:90%; height:auto;\" >...........since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+x ALIGN=MIDDLE  ALT=\"h+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this is the number of hot dogs\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%2828%29+=+-28%5E2+%2B+56%2A28+%2B+77 ALIGN=MIDDLE  ALT=\"P%2828%29+=+-28%5E2+%2B+56%2A28+%2B+77\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%2828%29+=-784+%2B+1568+%2B+77 ALIGN=MIDDLE  ALT=\"P%2828%29+=-784+%2B+1568+%2B+77\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%2828%29+=861 ALIGN=MIDDLE  ALT=\"P%2828%29+=861\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+y ALIGN=MIDDLE  ALT=\"k+=+y\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this is maximum profit\r<BR>\n" );
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document.write( "so, the vertex is at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" >)=(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28 ALIGN=MIDDLE  ALT=\"28\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=861 ALIGN=MIDDLE  ALT=\"861\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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