document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=631903>Question 631903</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The cost and revenue functions for selling a specialty item  are:<BR>\n" );
document.write( "	R(x) = 50x – 0.5 x2	\r<BR>\n" );
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document.write( "	C(x) = 4x + 10x2<BR>\n" );
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document.write( "	a)	Write the equation of the profit function P(x).<BR>\n" );
document.write( "	b)	Sketch the three functions C(x), R(x) and P(x) on the same set of axis.<BR>\n" );
document.write( "	c)	Determine the number of specialty items which produce a maximum profit.<BR>\n" );
document.write( "	d)	Find the maximum profit.<BR>\n" );
document.write( "	e)	Indicate on the profit curve the interval over which profit is decreasing.<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 #397881 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=397881\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Profit is Revenue minus Cost, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ P(x)\ =\ R(x)\ -\ C(x)\ =\ \left(50x\ -\ 0.5x^2\right)\ -\ \left(4x\ +\ 10x^2\right)\">\r<BR>\n" );
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document.write( "I'll lead the simplification and the graphing to you.\r<BR>\n" );
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document.write( "The profit function is a parabola that opens down.  The answer to part c is the value of the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\"> coordinate of the vertex, and the  answer to d is the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\"> coordinate of the vertex.\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" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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