document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1125542>Question 1125542</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Mrs. Inere can sell 50 brownie boxes each month if she charges $95 for each box. She estimates that for every $5 increase in price, she will sell 2 boxes less. Find the price that would yield the maximum revenue.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #741862 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=741862\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> she sells 50 brownie boxes when they are 95 dollars each.\r<BR>\n" );
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document.write( "her total revenue is 50 * 95 = 4750\r<BR>\n" );
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document.write( "she estimates that she will sell 2 boxes less for every 5 dollar incfrease in the price of 1 box.\r<BR>\n" );
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document.write( "the equation for that is y = (50 - 2x) * (95 + 5x).\r<BR>\n" );
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document.write( "each time x goes up 1 unit, the number of boxes goes down 2 and the price of each box goes up 5.\r<BR>\n" );
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document.write( "multiply the factors together to get y = 50 * 95 + 50 * 5x - 2x * 95 - 2x * 5x.\r<BR>\n" );
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document.write( "simplify to get y = 4750 + 250x - 190x - 10x^2\r<BR>\n" );
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document.write( "combine like terms to get y = 4750 + 60x - 10x^2\r<BR>\n" );
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document.write( "rearrange the terms in descending order of degree to get:\r<BR>\n" );
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document.write( "y - -10x^2 + 60x + 4750\r<BR>\n" );
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document.write( "this is a quadratic equation in standard form where:\r<BR>\n" );
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document.write( "a = -10<BR>\n" );
document.write( "b = 60<BR>\n" );
document.write( "c = 4750\r<BR>\n" );
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document.write( "the maximum value of this equation will occur when x = -b/(2a)\r<BR>\n" );
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document.write( "x = -b/(2a) becomes x = -60 / -20 = 3.\r<BR>\n" );
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document.write( "when x = 3, y = -10 * 3^2 + 60 * 3 + 4750 = 4840.\r<BR>\n" );
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document.write( "when x = 3, she sells 50 - 6 = 44 boxes at 95 + 15 = 110 dollars each for total revenue of 44 * 110 = 4840.\r<BR>\n" );
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document.write( "for her, it doesn't get any better than that.\r<BR>\n" );
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document.write( "here's the graph of the equation that shows when the maximum revenue occurs.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/100806.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "the blue line is the graph of the equations.\r<BR>\n" );
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document.write( "since the equations are equivalent, they draw the same line on the graph.\r<BR>\n" );
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document.write( "the orange line is there to show the value of the curve when x = 3.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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