document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1157181>Question 1157181</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​ total-revenue and​ total-cost functions, find the total​ profit, the maximum value of the total​ profit, and the value of x at which it occurs.\r<BR>\n" );
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document.write( "Upper R left parenthesis x right parenthesis equals 1200 x minus x squared<BR>\n" );
document.write( "R(x)=1200x−x2​, <BR>\n" );
document.write( "Upper C left parenthesis x right parenthesis equals 3000 plus 20 x<BR>\n" );
document.write( "C(x)=3000+20x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #780008 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=780008\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> r(x) = 1200x - x^2<BR>\n" );
document.write( "c(x) = 3000 + 20x<BR>\n" );
document.write( "p(x) = r(x) - c(x)<BR>\n" );
document.write( "that becomes:<BR>\n" );
document.write( "p(x) = 1200x - x^2 - (3000 + 20x)<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "p(x) = 1200x - x^2 - 3000 - 20x<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "p(x) = -3000 + 1180x - x^2<BR>\n" );
document.write( "order the terms in descending order of degree to get:<BR>\n" );
document.write( "p(x) = -x^2 + 1180x - 3000<BR>\n" );
document.write( "a = the coefficient of the x^2 term = -1<BR>\n" );
document.write( "b = the coefficient of the x term = 1180<BR>\n" );
document.write( "c = the constant term = -3000<BR>\n" );
document.write( "the maxim profit is when x = -b/2a.<BR>\n" );
document.write( "that becomes x = -1180/-2 = 590.<BR>\n" );
document.write( "the maximum profit is the value of the equation at x = 590<BR>\n" );
document.write( "that becomes p(x) = 345,100<BR>\n" );
document.write( "that's your solution.<BR>\n" );
document.write( "here's the graph that confirms that.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/042601.jpg\" alt=\"$$$\" ><BR>\n" );
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