document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1089655>Question 1089655</A>: <I><SPAN STYLE=\"word-break: break-all;\">  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #704085 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=704085\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formula is:\r<BR>\n" );
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document.write( "y = (x - 10,000 * x) * (20 + 4 * x) \r<BR>\n" );
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document.write( "y is the revenue.\r<BR>\n" );
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document.write( "x is the number of times that 10,000 is reduced from the price and also the number of times that 4 additional smartphones are sold.\r<BR>\n" );
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document.write( "for each reduction of 10,000 in the price of the smartphones, the number of additional smartphones sold is 4.\r<BR>\n" );
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document.write( "this is a quadratic equation that is most easily solved by using graphing software.\r<BR>\n" );
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document.write( "here's a picture of the graph of y = (120,000 - 10,000 * x) * (20 + 4 * x).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/080501.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "you can see from the graph that the maximum revenue is when x = 3.5.\r<BR>\n" );
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document.write( "you would want x to be greater than or equal to 0 since the number of smartphones sold can't be negative.\r<BR>\n" );
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document.write( "if you want to know how many smartphones are sold when revenue is equal to 2,400,000, just graph y = 2,400,000 and the intersection of that equation with the quadratic equation will tell you.\r<BR>\n" );
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document.write( "you will get y = 2,400,000 when x = 0 or when x = 7\r<BR>\n" );
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document.write( "here's a picture of the graph that shows the intersection of the equations of y = (120,000 - 10,000 * x) * (20 + 4 * x) and y = 2,400,000.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/080502.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "when you enter the equations into the graphing software, you remove the commas.\r<BR>\n" );
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document.write( "your solution is that revenue will be 2.4 million when x = 0 or when x = 7.\r<BR>\n" );
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document.write( "when x = 0, y = (120,000 - 10,000 * x) * (20 + 4 * x) becomes y = (120,000 - 0) * (20 + 0) which results in y = 120,000 * 20 which is equal to 2,400,000.\r<BR>\n" );
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document.write( "when x = 7, y = (120,00 - 10,000 * x) * (20 + 4 *  x) becomes y = (120,000 - 10,000 * 7) * (20 + 4 * 7) which becomes y = (120,000 - 70,000) * (20 + 28) which results in y = 50,000 * 48 which is equal to 2,400,000.\r<BR>\n" );
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document.write( "your solution is that a price of 120,000 or a price of 50,000 will result in total revenue of 2,400,000.\r<BR>\n" );
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document.write( "if you did not have graphing software, then you would use the quadratic formula.\r<BR>\n" );
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document.write( "before using the quadratic formula, you need to place the equation in standard form of:\r<BR>\n" );
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document.write( "0 = ax^2 + bx + c\r<BR>\n" );
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document.write( "when it's in this form, you get:\r<BR>\n" );
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document.write( "a = coefficient of the x^2 term.<BR>\n" );
document.write( "b = coefficient of the x term.<BR>\n" );
document.write( "c = the constant term.\r<BR>\n" );
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document.write( "your start with y = (120,000 - 10,000 * x) * (20 + 4 * x).\r<BR>\n" );
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document.write( "simplify by using the distributive law of multiplication to get:\r<BR>\n" );
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document.write( "y = 2,400,000 + 280,000 * x - 200,000 * x - 40,000 * x^2\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "y = 2,400,000 + 80,000 * x - 40,000 * x^2\r<BR>\n" );
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document.write( "since you want your revenue to be 2,400,000, replace y with 2,400,000 to get:\r<BR>\n" );
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document.write( "2,400,000 = 2,400,000 + 80,000 * x - 40,000 * x^2\r<BR>\n" );
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document.write( "to convert this to standard form, subtract 2,400,000 from both sides of the equation to get:\r<BR>\n" );
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document.write( "2,400,000 - 2,400,000 = 2,400,000 - 2,400,000 + 80,000 * x - 40,000 * x^2\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "0 = 80,000 * x - 40,000 * x^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( "0 = -40,000 * x^2 + 80,000 * x\r<BR>\n" );
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document.write( "the equation is now in standard form.\r<BR>\n" );
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document.write( "a = -40,000<BR>\n" );
document.write( "b = 80,000<BR>\n" );
document.write( "c = 0\r<BR>\n" );
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document.write( "to make the arithmetic simpler, you could divide both sides of this equation by 1000 to get:\r<BR>\n" );
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document.write( "0 = -40 * x^2 + 80 * x\r<BR>\n" );
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document.write( "a = -40<BR>\n" );
document.write( "b = 80<BR>\n" );
document.write( "c = 0\r<BR>\n" );
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document.write( "since it's still in standard form, you would use the quadratic formula to solve for x.\r<BR>\n" );
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document.write( "you will get x = 7 or x = 0.\r<BR>\n" );
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document.write( "that's the same solution we got when we looked at the graph of the intersection of the equation of y = (120,000 - 10,000 * x) * (20 + 4 * x) and y = 2,400,000.\r<BR>\n" );
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document.write( "the graphing software i used is at <a  rel=nofollow HREF= \"https://www.desmos.com/calculator\" target= \"_blank\">https://www.desmos.com/calculator</a>\r<BR>\n" );
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document.write( "the quadratic equation solver i used is at <a  rel=nofollow HREF= \"https://www.mathsisfun.com/quadratic-equation-solver.html\" target= \"_blank\">https://www.mathsisfun.com/quadratic-equation-solver.html</a>\r<BR>\n" );
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document.write( "information about the quadratic formula can be found at <a  rel=nofollow HREF= \"http://www.sosmath.com/algebra/quadraticeq/quadraformula/quadraformula.html\" target = \"_blank\">http://www.sosmath.com/algebra/quadraticeq/quadraformula/quadraformula.html</a>\r<BR>\n" );
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document.write( "i'll be available to answer any questions you might have regarding this.\r<BR>\n" );
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