document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1117851>Question 1117851</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The revenue function&#8203; R(x) and the cost function&#8203; C(x) for a particular product are given. These functions are valid only for the specified range of values. Find the number of units that must be produced to break even.\r<BR>\n" );
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document.write( "R(x)= 200x-x^2; C(x)=15x+6750 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #733026 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=733026\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> R(x) = 200x - x^2<BR>\n" );
document.write( "C(x) = 15x + 6750\r<BR>\n" );
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document.write( "to break even, R(x) = C(x).\r<BR>\n" );
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document.write( "that becomes:\r<BR>\n" );
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document.write( "200x - x^2 = 15x + 6750\r<BR>\n" );
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document.write( "subtract the right side of the equation from both sides of the equation to get:\r<BR>\n" );
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document.write( "200x - x^2 - 15x - 6750 = 0\r<BR>\n" );
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document.write( "combine like terms and re-arrange the terms in descending order of degree to get:\r<BR>\n" );
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document.write( "-x^2 + 185x - 6750 = 0\r<BR>\n" );
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document.write( "solve this quadratic equation to find the 0 points.\r<BR>\n" );
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document.write( "they will be at x = 50 or x = 135.\r<BR>\n" );
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document.write( "those are the number of units when you will break even.\r<BR>\n" );
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document.write( "between those 2 values, you will make money.\r<BR>\n" );
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document.write( "outside of those 2 values, you will lose money.\r<BR>\n" );
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document.write( "you should determine what the specified range of values are before answering, since not all of these may be in the specified range.\r<BR>\n" );
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document.write( "here's my graph of your equations showing the solution.\r<BR>\n" );
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document.write( "the first graph shows the intersection of the following 2 equations:\r<BR>\n" );
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document.write( "y = 200x - x^2 (your revenue equation)<BR>\n" );
document.write( "y = 15x + 6750 (your cost equation).\r<BR>\n" );
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document.write( "the intersection of these 2 equations shows the break even point.\r<BR>\n" );
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document.write( "that's when the revenue equals the cost.\r<BR>\n" );
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document.write( "the second graph shows the result of setting the 2 equations equal to each other and then subtracting the right side of the equation from both sides of the equation.\r<BR>\n" );
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document.write( "that equation is y = -x^2 + 185x - 6750.\r<BR>\n" );
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document.write( "when y = 0, that's your break even point.\r<BR>\n" );
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document.write( "here are the two graphs.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/052901.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/052902.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "to find the revenue and the cost at the break even point, simply replace x with the indicated values of 50 or 135 and you will find that the revenue and the cost are equal to each other.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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