document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1136545>Question 1136545</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The pear company sells pPhones. The cost to manufacture x pPhones is C(x)=-23x^2+50000x+20461 dollars (this includes overhead costs and production costs for each pPhone). If the company sells x pPhones for the maximum price they can fetch, the revenue function will be R(x)=-26x^2+128000x dollars. \r<BR>\n" );
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document.write( "How many pPhones should the pear company produce and sell to maximize profit? (remember that profit = revenue - cost)\r<BR>\n" );
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document.write( "Not sure how to solve this question. I could use some guidance on this problem... thank you. This is written by my professor.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #754328 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=754328\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> as a lesson in algebra, this problem is probably ok.\r<BR>\n" );
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document.write( "as a lesson in using algebra to solve practical, real world problems, this problem is probably not ok.\r<BR>\n" );
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document.write( "reality is not necessarily your prime concern in solving this problem, so we'll concentrate on the solving of the algebra first.\r<BR>\n" );
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document.write( "you have a revenue function and you have a cost function and you want a profit function.\r<BR>\n" );
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document.write( "profit = revenue minus cost, so if you subtract the cost function from the revenue function, you will get the profit function.\r<BR>\n" );
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document.write( "your revenue function is y = -26 * x^2 + 128000 * x.\r<BR>\n" );
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document.write( "your cost function is y = -23 * x^2 + 50000 * x + 20461.\r<BR>\n" );
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document.write( "your profit function will be y = -26 * x^2 + 128000 * x - (-23 * x^2 + 50000 * x + 20461).\r<BR>\n" );
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document.write( "simplify to get y = -26 * x^2 + 128000 * x - 23 * x^2 - 50000 * x - 20461.\r<BR>\n" );
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document.write( "combine like terms to get y = -3 * x^2 + 78000 * x - 20461.\r<BR>\n" );
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document.write( "that's your profit function.\r<BR>\n" );
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document.write( "you want to know when your profit will be maximum.\r<BR>\n" );
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document.write( "since this is a quadratic function that's in standard form, you get:\r<BR>\n" );
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document.write( "a = -3<BR>\n" );
document.write( "b = 78000<BR>\n" );
document.write( "c = -20461.\r<BR>\n" );
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document.write( "the maximum profit will be when x = -b / 2a.\r<BR>\n" );
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document.write( "that will be when x = -78000 / -6 = 13000.\r<BR>\n" );
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document.write( "when x = 13000, y = -3 * x^2 + 78000 * x - 20461 becomes y = -3 * 13000^2 + 78000 * 13000 - 20461 which becomes y = -507,000,000 + 1,014,000,000 - 20,461 = 506,979,539\r<BR>\n" );
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document.write( "your maximum profit will be when x = 13000 and will be 506 million, 979 thousand, 539 dollars.\r<BR>\n" );
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document.write( "that solves the algebra, which, once you know how to do it, is pretty straight forward.\r<BR>\n" );
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document.write( "now to using algebra to solve a realistic problem.\r<BR>\n" );
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document.write( "this problem is not ok for the following reason.\r<BR>\n" );
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document.write( "when x = 13000, .....\r<BR>\n" );
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document.write( "revenue = -2,730,000,000\r<BR>\n" );
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document.write( "cost = -3,236,979,539\r<BR>\n" );
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document.write( "profit = revenue minus cost = 506,979,539\r<BR>\n" );
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document.write( "you get your maximum profit when revenue is negative and cost is even more negative.\r<BR>\n" );
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document.write( "this is not realistic because both revenue and cost need to be positive.\r<BR>\n" );
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document.write( "but, that's not your worry.\r<BR>\n" );
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document.write( "your worry is to find the maximum profit which we found above.\r<BR>\n" );
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document.write( "i suppose somebody could make a case for the problem  being realistic, but i don't see it.\r<BR>\n" );
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document.write( "i created a spread sheet to show you the calculations for revenue, cost, and profit, for x in intervals of 1000.\r<BR>\n" );
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document.write( "it's shown below.\r<BR>\n" );
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document.write( "it also shows when the maximum revenue occurs and when the maximum cost occurs and when the maximum profit occurs.\r<BR>\n" );
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