document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=881317>Question 881317</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The demand equation for a certain product is given by p = 132 - 0.015x, where p is the unit price (in dollars) of the product and x is the number of units produced.  The total revenue obtained by producing and selling x units is given by R=xp.\r<BR>\n" );
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document.write( "Determine the prices that would yield a revenue of 9340 dollars\r<BR>\n" );
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document.write( "lowest price ___\r<BR>\n" );
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document.write( "highest price ___\r<BR>\n" );
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document.write( "I set up an equation 9430 = x(132-0.015x)\r<BR>\n" );
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document.write( "I thought I should solve for x and the substitute in to find p.<BR>\n" );
document.write( "-132/(2 X -0.015) = 4400\r<BR>\n" );
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document.write( "I substituted 4400 for x in p=132-0.015x thinking I would get the a price -- $66.00 that was wrong.\r<BR>\n" );
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document.write( "I also tried to solve the above equation with the quadratic formula and couldn't come up with the answer either.<BR>\n" );
document.write( "I put in 4400 and came up with 66 -- but that answer is neither the highest nor lowest price.<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 #532138 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=532138\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the solutions i came up with are:<BR>\n" );
document.write( "x = 71.335 and x = 8728.6642<BR>\n" );
document.write( "this was solved using the quadratic equation and also solved through graphing.\r<BR>\n" );
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document.write( "the equations that applied are:<BR>\n" );
document.write( "p = 132 - .015x<BR>\n" );
document.write( "that's your price equation.<BR>\n" );
document.write( "r = px<BR>\n" );
document.write( "that's your revenue equation.\r<BR>\n" );
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document.write( "you can substitute 132 - .015x for p in the revenue equation to get:\r<BR>\n" );
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document.write( "r = x * (132 - .015x)\r<BR>\n" );
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document.write( "simplify that to get:\r<BR>\n" );
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document.write( "r = 132x - .015x^2\r<BR>\n" );
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document.write( "you can graph that equation by substituting y for r.\r<BR>\n" );
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document.write( "the equation to graph is:\r<BR>\n" );
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document.write( "y = 132x - .015x^2\r<BR>\n" );
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document.write( "you can also graph the revenue equation of r = 9340 by graphing:\r<BR>\n" );
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document.write( "y = 9340\r<BR>\n" );
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document.write( "the intersection of these 2 equations on the graph will give you the values of x that will yield a revenue of 9340.\r<BR>\n" );
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document.write( "that graph is shown below:\r<BR>\n" );
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document.write( "in order to solve this equation using the quadratic formula, you had to set y = 9340 in the original equation of y = 132x - .015x^2 to get:<BR>\n" );
document.write( "9340 = 132x - .015x^2<BR>\n" );
document.write( "subtract 9340 from both sides of this equation to get:<BR>\n" );
document.write( "0 = 132x - .015x^2 - 9340 which can also be shown as:<BR>\n" );
document.write( "-.015x^2 + 132x - 9340 = 0\r<BR>\n" );
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document.write( "that equation is now in standard form and you get:<BR>\n" );
document.write( "a = -.015<BR>\n" );
document.write( "b = 132<BR>\n" );
document.write( "c = -9340\r<BR>\n" );
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document.write( "now you can apply the quadratic formula of:<BR>\n" );
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document.write( "               x = -b +/- sqrt(b^2 - 4ac)\r\n" );
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document.write( "                            2a\r\n" );
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document.write( "the result of those calculations will get you:\r<BR>\n" );
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document.write( "x = 71.3358 or x = 8728.66\r<BR>\n" );
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document.write( "the value of x = 4400 is the value of the axis of symmetry which leads to the maximum point on the graph when you replace x in the original equation with 4400.\r<BR>\n" );
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document.write( "that would be the equation of y = 132x - .015x^2 which becomes y = 132(4400) - .015(4400)^2.\r<BR>\n" );
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document.write( "the result of that evaluation leads to the maximum point on the graph of 290400.\r<BR>\n" );
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