document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=998970>Question 998970</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Karen runs a print shop that makes posters for large companies. It is a very competitive business. The market price is currently $1.00 per poster. She has fixed costs of $500.00. Her variable costs are $1,500 for the first thousand posters, $1,200 for the second thousand, and then $800 for each additional thousand posters.What is her ATC per poster if she prints 1,000?<BR>\n" );
document.write( "What is her ATC per poster if she prints 2,000?<BR>\n" );
document.write( "What is her ATC per poster if she prints 10,000? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #616694 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=616694\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> her revenue is 1 dollar * the number of posters she sells.\r<BR>\n" );
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document.write( "her cost will vary depending on the number of posters she prints.\r<BR>\n" );
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document.write( "her costs are:\r<BR>\n" );
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document.write( "500 fixed.<BR>\n" );
document.write( "1500 for the first 1000 posters / 1000 = 1.5 for each poster.<BR>\n" );
document.write( "1200 for the second 1000 posters = 1.2 for each poster.<BR>\n" );
document.write( "800 for each additional 1000 posters above 2000 / 1000 = .8 for each poster.\r<BR>\n" );
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document.write( "if she prints 1000 posters, her total cost will be:\r<BR>\n" );
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document.write( "500 + 1000 * 1.5 which becomes:<BR>\n" );
document.write( "500 + 1500 which becomes:<BR>\n" );
document.write( "2000.\r<BR>\n" );
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document.write( "her total cost is 2000 if she prints 1000 posters.\r<BR>\n" );
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document.write( "500 is her fixed cost.<BR>\n" );
document.write( "1500 is the cost for the first 1000 posters.\r<BR>\n" );
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document.write( "if she prints 2000, her total cost will be:\r<BR>\n" );
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document.write( "500 + 1.5 * 1000 + 1.2 * (2000 - 1000) which becomes:<BR>\n" );
document.write( "500 + 1500 + 1.2 * 1000 which becomes:<BR>\n" );
document.write( "500 + 1500 + 1200 which becomes:<BR>\n" );
document.write( "3200.\r<BR>\n" );
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document.write( "her total cost is 3200 is she prints 2000 posters.\r<BR>\n" );
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document.write( "if she prints 10,000, her total cost will be:\r<BR>\n" );
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document.write( "500 + 1.5 * 1000 + 1.2 * 1000 + .8 * (10,000 - 2000) which becomes:<BR>\n" );
document.write( "500 + 1500 + 1200 + .8 * (8000) which becomes:<BR>\n" );
document.write( "500 + 1500 + 1200 + 6400 which becomes:<BR>\n" );
document.write( "3200 + 6400 which becomes:<BR>\n" );
document.write( "9600\r<BR>\n" );
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document.write( "her total cost is 9600 if she prints 10,000 posters.\r<BR>\n" );
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document.write( "500 is her fixed cost.<BR>\n" );
document.write( "1500 is the cost for the first 1000 posters.<BR>\n" );
document.write( "1200 is the cost for the next 1000 posters.<BR>\n" );
document.write( "6400 is the cost for the last 8000 posters.\r<BR>\n" );
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document.write( "her average cost is calculated as follows:\r<BR>\n" );
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document.write( "if she prints 1000 posters, her average cost is 2000 / 1000 = 2 dollars per poster.\r<BR>\n" );
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document.write( "if she prints 2000 posters, her average cost is 3200 / 2000 = 1.6 dollars per poster.\r<BR>\n" );
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document.write( "if she prints 10,000 posters, her average cost is 9600 / 10,000 = .96 dollars per poster.\r<BR>\n" );
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document.write( "if she can only make 1 dollar per poster, she's losing money unless she sells something very close to 10,000 posters.\r<BR>\n" );
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document.write( "THE FOLLOWING IS EXTRA THAT I DON'T THINK YOU NEED TO KNOW TO SOLVE YOUR PROBLEM, BUT IT IS INTERESTING TO SEE HOW THE BREAK EVEN POINT WOULD BE CALCULATED IN THIS PROBLEM.\r<BR>\n" );
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document.write( "READ ON IF INTERESTED.\r<BR>\n" );
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document.write( "STOP HERE IF NOT.\r<BR>\n" );
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document.write( "you can solve for her break-even point as follows:\r<BR>\n" );
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document.write( "the break even point is when the revenue is equal to the cost.\r<BR>\n" );
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document.write( "since we know she has to sell more than 2000, the equation becomes:\r<BR>\n" );
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document.write( "revenue = cost.\r<BR>\n" );
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document.write( "revenue = 1 * x, where x is the number of posters sold.\r<BR>\n" );
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document.write( "cost = 3200 + (x - 2000) * .8\r<BR>\n" );
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document.write( "the 3200 is the total cost for the first 2000 posters.\r<BR>\n" );
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document.write( "revenue = cost becomes:\r<BR>\n" );
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document.write( "1 * x = 3200 + (x - 2000) * .8\r<BR>\n" );
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document.write( "remove parentheses to get:\r<BR>\n" );
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document.write( "1 * x = 3200 + .8 * x - 2000 * .8\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "1 * x = 3200 + .8 * x - 1600\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "1 * x = .8 * x + 1600.\r<BR>\n" );
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document.write( "subtract .8 * x from both sides of the equation to get:\r<BR>\n" );
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document.write( "x - .8 * x = 1600\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( ".2 * x = 1600\r<BR>\n" );
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document.write( "divide both sides of this equation by .2 to get:\r<BR>\n" );
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document.write( "x = 1600 / .2 = 8000.\r<BR>\n" );
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document.write( "she would break even if she printed and sold 8000 posters.\r<BR>\n" );
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document.write( "her revenue would be 8000.\r<BR>\n" );
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document.write( "her cost would be 500 + 1500 + 1200 + .8 * (8000 - 2000) which becomes:<BR>\n" );
document.write( "500 + 1500 + 1200 .8 * 6000 which becomes:<BR>\n" );
document.write( "3200 + 4800 which becomes:<BR>\n" );
document.write( "8000.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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