document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=231428>Question 231428</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An automobile manufacturer can produce up to 300 cars per day.  The profit made from the sale of these vehicles can be modeled by the function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=-10x%5E2%2B3500x-66000 ALIGN=MIDDLE  ALT=\"P%28x%29=-10x%5E2%2B3500x-66000\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Where P(x) is the profit in dollars and x is the number of automobiles made and sold.  How many cars should be made and sold to maximize profits.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #171287 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=171287\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What you have is a quadratic formula in the form of ax^2 + bx + c where:\r<BR>\n" );
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document.write( "a = -10<BR>\n" );
document.write( "b = 3500<BR>\n" );
document.write( "c = -66000\r<BR>\n" );
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document.write( "Since a is negative, this quadratic equation opens downward.\r<BR>\n" );
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document.write( "The max point is at x = -b/2a\r<BR>\n" );
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document.write( "That would be at x = -3500/-20 = 175.\r<BR>\n" );
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document.write( "When x = 175, y = -10*175^2 + 3500*175 - 66000 = 240250\r<BR>\n" );
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document.write( "Maximum profit attained is $240250.\r<BR>\n" );
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document.write( "This happens when 175 cars are sold.\r<BR>\n" );
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document.write( "graph of this equation looks like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-50%2C350%2C-100000%2C300000%2C-10x%5E2%2B3500x-66000%2C240250%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-50%2C350%2C-100000%2C300000%2C-10x%5E2%2B3500x-66000%2C240250%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "As can be seen, the graph peaks at x = 175.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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