document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203526>Question 1203526</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). The one-time fixed costs will total . The variable costs will be  per book. The publisher will sell the finished product to bookstores at a price of  per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #839165 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=839165\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x equal the number of books produced and sold.<BR>\n" );
document.write( "let c = total cost<BR>\n" );
document.write( "let f = fixed cost<BR>\n" );
document.write( "let v = vriable cost<BR>\n" );
document.write( "let s = sale price per book.<BR>\n" );
document.write( "let r = total revenue<BR>\n" );
document.write( "let p = total profit.\r<BR>\n" );
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document.write( "your equations are:\r<BR>\n" );
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document.write( "c = f + x * v<BR>\n" );
document.write( "r = x * s<BR>\n" );
document.write( "p = r - c\r<BR>\n" );
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document.write( "you break even when p = 0<BR>\n" );
document.write( "when p = 0, you get 0 = r - c<BR>\n" );
document.write( "add c to both sides of the equaiton and you get c = r<BR>\n" );
document.write( "switch sides and you get r = c.\r<BR>\n" );
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document.write( "assuming r = c, then:<BR>\n" );
document.write( "replace r with x * s and replace c with f + x * v<BR>\n" );
document.write( "you get x * s = f + x * v<BR>\n" );
document.write( "subtract x * v from both sides of the equation to get:<BR>\n" );
document.write( "x * s - x * v = f<BR>\n" );
document.write( "that's your break even equation.<BR>\n" );
document.write( "when that occurs, your revenue from sales will equal your total production costs.\r<BR>\n" );
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document.write( "as an example:<BR>\n" );
document.write( "asume f = 5000 and v = 2.5 amd s = 3<BR>\n" );
document.write( "break even is when r = c<BR>\n" );
document.write( "that becomes when x * s = f + x * v<BR>\n" );
document.write( "since f = 5000 and v = 2.5 and s = 3, the equation becomes:<BR>\n" );
document.write( "x * 3 = 5000 + x * 2.5<BR>\n" );
document.write( "subtract x * 2.5 from both sides of the equation to get x * 3 - x * 2.5 = 5000<BR>\n" );
document.write( "simplify to get .5 * x = 5000<BR>\n" );
document.write( "solve for x to get x = 5000 / .5 = 10,000\r<BR>\n" );
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document.write( "you will break even when you produce and sell 10,000 books.<BR>\n" );
document.write( "your revenue will be 10,000 * 3 = 30,000<BR>\n" );
document.write( "your production cost will be 5000 + 2.5 * 10,000 = 5000 = 25,000 = 30,000<BR>\n" );
document.write( "total sales = total cost = break even.<BR>\n" );
document.write( "your profit will be 0 at break even point.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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