document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=425780>Question 425780</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to find a profit function out of this word problem:\r<BR>\n" );
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document.write( "Hercules Films is also deciding on the price of the video release of it's film Bride of the son of Frankenstein. Again, marketing estimates that at a price of p dollars it can sell q=324000-18000p copies, but each copy cost $4 to make. What price will give the greatest profit?\r<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 #296352 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=296352\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hercules Films is also deciding on the price of the video release of it's film Bride of the son of Frankenstein. Again, marketing estimates that at a price of p dollars it can sell q=324000-18000p copies, but each copy cost $4 to make. What price will give the greatest profit? <BR>\n" );
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document.write( "Profit = Revenue-Cost<BR>\n" );
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document.write( "Revenue = p(324000-p)<BR>\n" );
document.write( "Cost = 4p<BR>\n" );
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document.write( "Profit = p(324000-p)-4p<BR>\n" );
document.write( "Profit = 323996p - p^2<BR>\n" );
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document.write( "That is a quadratic with a = -1 and b = 323996<BR>\n" );
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document.write( "Maximum profit occurs when p = -b/(2a) = -323996/(-2) = $161,998<BR>\n" );
document.write( "That price will give the greatest profit.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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