document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=188911>Question 188911</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The marketing department at the John Deere company has found that the revenue from the sales of heavy-duty tractors is a function of the unit price, p, in dollars  If the revenue, R is given by <BR>\n" );
document.write( "R(p) = - p2 + 1900p\r<BR>\n" );
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document.write( "What unit price should be established in order to maximize revenue?  (use the vertex formula.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #141815 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=141815\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "The <i>x</i>-coordinate of the vertex of a parabola whose equation is in the form:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f(x) = ax^2 + bx + c\">\r<BR>\n" );
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document.write( "is given by:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x_V = \frac{-b}{2a}\">\r<BR>\n" );
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document.write( "For your given function,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ R(p) = -p^2 + 1900p\">\r<BR>\n" );
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document.write( "<i>a</i> = -1 and <i>b</i> = 1900, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ p_V = \frac{-1900}{2(-1)} = 950\">\r<BR>\n" );
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document.write( "Hence the unit price to maximize revenue is $950.  Less than a thousand dollars for a new heavy duty John Deere tractor?  Is someone nuts?  Fire the marketing guy who came up with that revenue function.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ R(p) = -p^2 + 190000p\">\r<BR>\n" );
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document.write( "giving a max revenue price of $95,000 - that I might believe.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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document.write( " </SPAN>\n" );
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