document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=161544>Question 161544</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm having a hard time setting up this equation...<BR>\n" );
document.write( "A manufacturer finds that for the first 300 units of its product that are produced and sold, the profit is $60 per unit. The profit on each of the units  beyond 300 is decreased by $0.10 times the number of additional units sold. What level of output will maximize profit?\r<BR>\n" );
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document.write( "I can solve these when I am givin the function but I need help setting this one up. Then I will be more well equipped to solve these in the future.\r<BR>\n" );
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document.write( "Thanks to all the tutors out there, your help is greatly appreciated. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #119010 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=119010\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A manufacturer finds that for the first 300 units of its product that are produced and sold, the profit is $60 per unit. The profit on each of the units beyond 300 is decreased by $0.10 times the number of additional units sold. What level of output will maximize profit?<BR>\n" );
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document.write( "For the 1st 300, Profit = 300*60<BR>\n" );
document.write( "For all over 300, the profit is $60 - $0.10 times the number sold, = $60 - $0.10*(x-300).<BR>\n" );
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document.write( "Overall then, <BR>\n" );
document.write( "Profit = 300*60 + (x-300)*(60 - 0.1(x-300))<BR>\n" );
document.write( "P = 18000 + (x-300)*(60 - 0.1x + 30)<BR>\n" );
document.write( "P = 18000 + (x-300)*(-0.1x + 90)<BR>\n" );
document.write( "P = 18000 -0.1x^2 + 120x - 27000<BR>\n" );
document.write( "P = -0.1x^2 + 120x - 9000<BR>\n" );
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document.write( "To find the max, set the 1st derivative = 0<BR>\n" );
document.write( "0 = -0.2x + 120<BR>\n" );
document.write( "0.2x = 120<BR>\n" );
document.write( "x = 600 <BR>\n" );
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