document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1168738>Question 1168738</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A company produces very unusual cd’s for which the variable cost is $17 per CD and the fixed cost are $35000. They will sell the cd’s for $49 each. Let x be the number of cd’s produced. Write the total cost C as a function of the number of cd’s produced. <BR>\n" );
document.write( "C=$_______<BR>\n" );
document.write( "Write the total revenue R as a function of the number of cd’s produced. <BR>\n" );
document.write( "R=$_______<BR>\n" );
document.write( "Write the total profit P as a function of the number of cd’s produced <BR>\n" );
document.write( "P=$___________<BR>\n" );
document.write( "Find the number of cd’s which must be produced to break even. <BR>\n" );
document.write( "The number of cd’s in which must be produced to break even is __________  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #793348 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=793348\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = the number of CD's.\r<BR>\n" );
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document.write( "your cost function is:\r<BR>\n" );
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document.write( "C = 35000 + 17*x\r<BR>\n" );
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document.write( "35000 is the fixed cost.<BR>\n" );
document.write( "17*x is the variable cost.\r<BR>\n" );
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document.write( "the fixed cost is the same regardless of how many CD's are sold.<BR>\n" );
document.write( "the variable cost is the additional cost for each CD that is produced.<BR>\n" );
document.write( "x represents the number of CD's that are produced.\r<BR>\n" );
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document.write( "your revenue function is:\r<BR>\n" );
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document.write( "R = 49*x\r<BR>\n" );
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document.write( "it is a variable cost only.<BR>\n" );
document.write( "it represents the revenue received for each CD that is sold.<BR>\n" );
document.write( "x represents the number of CD's that are sold.\r<BR>\n" );
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document.write( "the built in assumption of the problem is that the number of CD's sold is the same as the number of CD's produced.\r<BR>\n" );
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document.write( "that's why x represents the number of CD's in both the cost function and the revenue function.\r<BR>\n" );
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document.write( "your profit function is:\r<BR>\n" );
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document.write( "P = (49 * x) - (35000 + 17 * x).\r<BR>\n" );
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document.write( "P represents the profit.\r<BR>\n" );
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document.write( "(49 * x) represents the revenue.\r<BR>\n" );
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document.write( "(35000 + 17 * x) represents the cost.\r<BR>\n" );
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document.write( "profit is equal to revenue minus cost.\r<BR>\n" );
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document.write( "the equation reflects that.\r<BR>\n" );
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document.write( "to break even, the profit must be equal to 0.\r<BR>\n" );
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document.write( "if the profit was positive, you made mooney.<BR>\n" );
document.write( "if the profit was negative, you lost money.<BR>\n" );
document.write( "when the profit is 0, you didn't make money and you didn't lose money.<BR>\n" );
document.write( "you just broke even.<BR>\n" );
document.write( "that's why it's called the break even point.\r<BR>\n" );
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document.write( "to find how many CD's needed to be produced and sold to break even, set the profit equation equal to 0.\r<BR>\n" );
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document.write( "your profit equation of P = 49 * x - (35000 + 17 * x) becomes:\r<BR>\n" );
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document.write( "0 = 49 * x - (35000 + 17 * x)\r<BR>\n" );
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document.write( "simplify the equation by removing the parentheses to get:\r<BR>\n" );
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document.write( "0 = 49 * x - 35000 - 17 * x\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "0 = 32 * x - 35000\r<BR>\n" );
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document.write( "add 35000 to both sides of the equation to get:\r<BR>\n" );
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document.write( "35000 = 32 * x\r<BR>\n" );
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document.write( "divide both sides of the equation by 32 to get:\r<BR>\n" );
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document.write( "35000 / 32 = x\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x = 35000 / 32 = 1093.75\r<BR>\n" );
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document.write( "the number of CD's that must be produced and sold to break even is 1093.75\r<BR>\n" );
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document.write( "if you are still confused by any of this, let me know which part confuses you and i'll work to clear up the confusion as best i can.\r<BR>\n" );
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document.write( "theo\r<BR>\n" );
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document.write( " </SPAN>\n" );
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