document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1175620>Question 1175620</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 8. The daily price-demand equation for whole milk in a chain of supermarkets is<BR>\n" );
document.write( "q = 8000  -  400p<BR>\n" );
document.write( "where p is the price per gallon and q is the number of gallons sold per day. Find the<BR>\n" );
document.write( "price that will produce a revenue of (a) $40,000 and (b) $42,000. Round answer to two<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 #801435 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=801435\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your equation is:\r<BR>\n" );
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document.write( "q = 8000 - 400p\r<BR>\n" );
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document.write( "q = the numbe of gallons of milk sold each day.\r<BR>\n" );
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document.write( "p = the price per gallon.\r<BR>\n" );
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document.write( "revenue equals quantity * price.\r<BR>\n" );
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document.write( "if r = revenue and q = quantity and p = price, then the formula becomes:\r<BR>\n" );
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document.write( "r = q * p\r<BR>\n" );
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document.write( "since q = 8000 - 400p, you can replace q in that equation with it's equivalent value in terms of p to get:\r<BR>\n" );
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document.write( "r = (8000 - 400p) * p\r<BR>\n" );
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document.write( "simplify this equation to get:\r<BR>\n" );
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document.write( "r = 8000p - 400p^2.\r<BR>\n" );
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document.write( "when revenue = 40,000, the equation becomes:\r<BR>\n" );
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document.write( "40000 = 8000p - 400p^2.\r<BR>\n" );
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document.write( "add 400p^2 to both sides of this equation and subtract 8000p from both sides of this equation and order the terms in descending order of degree to get:\r<BR>\n" );
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document.write( "400p^2 - 8000p + 40000 = 0\r<BR>\n" );
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document.write( "factor this quadratic equationt to get:\r<BR>\n" );
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document.write( "p = 10.\r<BR>\n" );
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document.write( "raise the revenue to 42000 and do the samething you did when it was 40000 to get:\r<BR>\n" );
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document.write( "400p^2 - 8000p + 42000 = 0\r<BR>\n" );
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document.write( "factor this quadratic equation and you will find that the roots of this equation are complex and not real.\r<BR>\n" );
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document.write( "something is obviously wrong.\r<BR>\n" );
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document.write( "go back to the original revenue equation that was:\r<BR>\n" );
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document.write( "r = 8000p - 400p^2.\r<BR>\n" );
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document.write( "arrange the terms in descending order of degree to get:\r<BR>\n" );
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document.write( "r = -400p^2 + 8000p\r<BR>\n" );
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document.write( "set r equal to 0 and you get:\r<BR>\n" );
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document.write( "-400p^2 + 8000p = 0\r<BR>\n" );
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document.write( "the equation is now in standard form of ax^2 + bx + c = 0\r<BR>\n" );
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document.write( "a = -400<BR>\n" );
document.write( "b = 8000<BR>\n" );
document.write( "c = 0\r<BR>\n" );
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document.write( "the maximum / minimum value of a quadratic equation is determined by the formula of:\r<BR>\n" );
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document.write( "x = -b/2a\r<BR>\n" );
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document.write( "in this equation, p replaced x, so the maximum / minimum value of the quadratic equation is obtained by the formula of:\r<BR>\n" );
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document.write( "p = -b/2a.\r<BR>\n" );
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document.write( "solve for p to get:\r<BR>\n" );
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document.write( "p = -8000 / -800 = 10\r<BR>\n" );
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document.write( "the maximum value of the quadratic equation is when p = 10.\r<BR>\n" );
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document.write( "replace p in the revenue eqution of r = -400p^2 + 8000p to get:\r<BR>\n" );
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document.write( "r = 40,000.\r<BR>\n" );
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document.write( "that explains why the roots weren't real when you changed the revenue from 40,000 to 42,000.\r<BR>\n" );
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document.write( "you could not obtain a revenue of 42,000 because the maximum revenue of the equation was 40,000.\r<BR>\n" );
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document.write( "a graph of the equation also shows this to be true, as shown below.\r<BR>\n" );
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document.write( "y = 40,000 intersects the equation at x = 10.\r<BR>\n" );
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document.write( "y = 42,000 doesn't intersect the equation at all.\r<BR>\n" );
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document.write( "here's the graph.\r<BR>\n" );
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