document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1011054>Question 1011054</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Say a car company sells 20 cars each week at a price of $6400 each. The sales department says that for every increase in $300 in price, sales will fall by one car. The dealer's cost of each car is $4000. What price will maximize the profit for the company? What will be the equation be arranged as?\r<BR>\n" );
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document.write( "I know that profit is equal to revenue minus expenses but I dont know how to arrange the quadratic equation. Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #626606 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=626606\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = the number of cars that will not be sold if the price increases by 300 dollars a car.\r<BR>\n" );
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document.write( "let 300x = the number of times the price of a car will be increased by 300 dollars.\r<BR>\n" );
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document.write( "the dealer's cost is 4000 per car.\r<BR>\n" );
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document.write( "the dealer's profit is the sale price of the car minus the cost.\r<BR>\n" );
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document.write( "profit equals revenue minus cost.\r<BR>\n" );
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document.write( "the formula for profit will therefore be:\r<BR>\n" );
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document.write( "profit = (6400 + 300x) * (20 - x) - 4000 * (20 - x)\r<BR>\n" );
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document.write( "let's see what happens:\r<BR>\n" );
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document.write( "when x = 0:<BR>\n" );
document.write( "profit = 6400 * 20 - 4000 * 20 = 48000\r<BR>\n" );
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document.write( "when x = 1:<BR>\n" );
document.write( "profit = 6700 * 19 - 4000 * 19 = 51300\r<BR>\n" );
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document.write( "when x = 2:<BR>\n" );
document.write( "profit = 7000 * 18 - 4000 * 18 = 54000\r<BR>\n" );
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document.write( "etc.\r<BR>\n" );
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document.write( "the equation of profit = (6400 + 300x) * (20 - x) - 4000 * (20 - x) is a quadratic equation.\r<BR>\n" );
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document.write( "simplify it to see what it comes out to be.\r<BR>\n" );
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document.write( "after simplification, the equation becomes profit = -300x^2 + 3600x + 48000.\r<BR>\n" );
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document.write( "this is a quadratic equation in standard form.\r<BR>\n" );
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document.write( "since the standard form of a quadration equation is ax^2 + bx + c = 0, then set this equation to 0 and solve using the quadratic formula amd / or the formula for finding the max / min point of the quadratic equation.\r<BR>\n" );
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document.write( "you can also graph the equation to see what it looks like.\r<BR>\n" );
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document.write( "setting the equation to 0, you get -300x^2 + 3600x + 48000 = 0\r<BR>\n" );
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document.write( "this results in:\r<BR>\n" );
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document.write( "a = -300<BR>\n" );
document.write( "b = 3600<BR>\n" );
document.write( "c = 48000\r<BR>\n" );
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document.write( "the quadratic formuls is:\r<BR>\n" );
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document.write( "                 x = (-b plus or minus sqrt(b^2 - 4ac)\r\n" );
document.write( "                     ---------------------------------\r\n" );
document.write( "                                  (2a)\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "the formula for the value of x for the max / min point is:\r<BR>\n" );
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document.write( "                  x = (-b)\r\n" );
document.write( "                      ----\r\n" );
document.write( "                      (2a)\r\n" );
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document.write( "you can solve using these equations, or you can graph the equation and, if you have the right software, it will tell you what the solutions are.\r<BR>\n" );
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document.write( "the right software in this case, would be http://www.desmos.com/calculator.\r<BR>\n" );
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document.write( "there may be others, but this one is pretty good and fairly easy to use.\r<BR>\n" );
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document.write( "the graph of the equation looks like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/121901.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "if you solved using the formula, you would get the same answers.\r<BR>\n" );
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document.write( "when x = 0, the profit is 48000.<BR>\n" );
document.write( "the profit is max at x = 6 when the profit is 58800.<BR>\n" );
document.write( "the profit is 0 when x = 20.<BR>\n" );
document.write( "on the graph, y represents the profit.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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