document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1167949>Question 1167949</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The demand equation for a certain product is given by p = 118 −0.045x, where p is the unit price (in dollars) of the product and x is the number of units produced. <BR>\n" );
document.write( "The total revenue obtained by producing and selling x units is given by R = x*p.\r<BR>\n" );
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document.write( "Determine prices (p) that would yield a revenue of 9200 dollars.\r<BR>\n" );
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document.write( "Lowest such price = ? dollars<BR>\n" );
document.write( "Highest such price = ? dollars\r<BR>\n" );
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document.write( "Please help me with this!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #792580 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=792580\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> not sure if this is right, but this is what i get.\r<BR>\n" );
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document.write( "R = x * p\r<BR>\n" );
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document.write( "p = 118 - .045x\r<BR>\n" );
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document.write( "p in both equation equals the price per unit.\r<BR>\n" );
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document.write( "if you replace p in the first equation with its equivalent value of 118 - .045x, then you get:\r<BR>\n" );
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document.write( "R = x * (118 - .045x)\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "R = 118 * x - .045 * x^2\r<BR>\n" );
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document.write( "if you replace R with y, the equation becomes y = 118 * x - .045 * x^2\r<BR>\n" );
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document.write( "y represents the revenue, just like R represented the revenue.\r<BR>\n" );
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document.write( "this allows the equation to be graphed more easily, since a lot of graphing software assumes the vertical axis is the y-axis and the horizontal axis is the x-axis.\r<BR>\n" );
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document.write( "if we reorder the terms in descending order of degree and switch sides, the equation remains the same, but is shown as:\r<BR>\n" );
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document.write( "-.045 * x^2 + 118 * x = y\r<BR>\n" );
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document.write( "if we want the revenue to be equal to 9200, we set y equal to 9200 and we get:\r<BR>\n" );
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document.write( "-.045 * x^2 + 118 * x = 9200\r<BR>\n" );
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document.write( "if we want to solve this quadratic equation, we subtract 9200 from both sides to get:\r<BR>\n" );
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document.write( "-.045 * x^2 + 118 * x - 9200 = 0\r<BR>\n" );
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document.write( "when we solve this quadratic equation, we get:\r<BR>\n" );
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document.write( "x = 80.43328924441 or x = 2541.7889329778\r<BR>\n" );
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document.write( "those values of x make the equation true.\r<BR>\n" );
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document.write( "if we add 9200 to both sides of the equation, the equation is still true.\r<BR>\n" );
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document.write( "we get:\r<BR>\n" );
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document.write( "-.045 * x^2 + 118 * x = 9200\r<BR>\n" );
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document.write( "what all this is saying is that when x = 80.43328924441 or x = 2541.7889329778, y = 9200, which is saying that the revenue is equal to 9200.\r<BR>\n" );
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document.write( "we have values of x, but we don't have values of p.\r<BR>\n" );
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document.write( "we know that x * p = revenue, so we solve for p by dividing 9200 by x.\r<BR>\n" );
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document.write( "we get:\r<BR>\n" );
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document.write( "9200 / 80.43328924441 = 114.38050198\r<BR>\n" );
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document.write( "9200 / 2541.7889329778 = 3.61949802\r<BR>\n" );
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document.write( "i didn't round because, if you wanted to check if the arithmetic is correct, you would have to use the unrounded numbers or you would come up with some small discrepancies.\r<BR>\n" );
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document.write( "i will round now, since i showed you what the unrounded numbers are.\r<BR>\n" );
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document.write( "the number of units probably should be rounded to the nearest unit.\r<BR>\n" );
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document.write( "the money probably should be rounded to the nearest penny.\r<BR>\n" );
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document.write( "after doing that, you get:\r<BR>\n" );
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document.write( "if you produce about 80 units, the price per unit should be about 114.38.\r<BR>\n" );
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document.write( "if you produce about 2542 units, the price per unit should be about 3.62 \r<BR>\n" );
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document.write( "both the demand equation and the revenue equation are satisfied when x = 80.43328924441 or x = 2541.7889329778\r<BR>\n" );
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document.write( "demand equation is p = 118 - .045 * x<BR>\n" );
document.write( "when x = 80.43328924441, p = 114.38050198<BR>\n" );
document.write( "when x = 2541.78893298, p = 3.61949802\r<BR>\n" );
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document.write( "revenue equation is r = x * p<BR>\n" );
document.write( "when r = 9200, the equation becomes 9200 = x * p<BR>\n" );
document.write( "when x = 80.43328924441, p = 114.38050198<BR>\n" );
document.write( "when x = 2541.78893298, p = 3.61949802\r<BR>\n" );
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document.write( "both the demand equation and the revenue equation are satisfied with those number.\r<BR>\n" );
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document.write( "that's the best i can do.<BR>\n" );
document.write( "i think it's right, but i always allow for the possibility that i could be wrong.\r<BR>\n" );
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document.write( "good luck with it.\r<BR>\n" );
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document.write( "hopefully this helps.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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