document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1058425>Question 1058425</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Total profit P is the difference between total revenue R and total cost C. Given the following&#8203; total-revenue and&#8203; total-cost functions, find the total&#8203; profit, the maximum value of the total&#8203; profit, and the value of x at which it occurs..\r<BR>\n" );
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document.write( "R(x)= 1200x-(x squared)\r<BR>\n" );
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document.write( "C(x)= 3100+20x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #673478 by </B><A HREF=/tutors/aboutme.mpl?userid=solve_for_x><B>solve_for_x(190)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solve_for_x><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=673478\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The profit function is:\r<BR>\n" );
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document.write( "P(x) = R(x) - C(x)\r<BR>\n" );
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document.write( "P(x) = (1200x - x^2) - (3100 + 20x)\r<BR>\n" );
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document.write( "P(x) = -x^2 + 1200x - 20x - 3100\r<BR>\n" );
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document.write( "P(x) = -x^2 + 1180x - 3100\r<BR>\n" );
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document.write( "This is the equation of a parabola that opens downward. The maximum value of the profit<BR>\n" );
document.write( "corresponds to the vertex of the parabola.\r<BR>\n" );
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document.write( "The x-coordinate of the vertex is:\r<BR>\n" );
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document.write( "x = -b/2a = (-1180) / (-1*2) = 590\r<BR>\n" );
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document.write( "The function value at the vertex is then:\r<BR>\n" );
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document.write( "P(590) = -(590)^2 + 1198(590) - 3100\r<BR>\n" );
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document.write( "P(590) = 345,000\r<BR>\n" );
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document.write( "Solution:\r<BR>\n" );
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document.write( "Total profit = -x^2 + 1180x - 3100\r<BR>\n" );
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document.write( "Maximum profit = 345,000, at x = 590 </SPAN>\n" );
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