document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=510130>Question 510130</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Your club is selling candles to raise money. It costs $100 to rent a booth to sell candles.  If the candles cost $1 each and are sold for $5 each, how many candle must be sold to equal your expenses? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #341727 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=341727\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The cost as a function of the number of candles bought is 1 dollar per candle bought plus 100 dollars for the rental of the booth.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x_b\"> represent the number of candles bought, then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large C(x_b)\ =\ x_b\ +\ 100\">.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x_s\"> represent the number sold and this number is restricted to <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x_s\ \leq\ x_b\"> since you can't sell more than you buy.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The revenue received is 5 dollars per candle sold, so the revenue function is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 5x_s\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Profit is Revenue minus Cost, so:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ P(x_b,x_s)\ =\ 5x_s\ -\ \left(x_b\ +\ 100\right)\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Breakeven, that is when profit equals zero is when cost equals revenue:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x_s\ =\ \frac{x_b\ +\ 100}{5}\"> \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now if what you really wanted to know (but didn't ask, or didn't communicate effectively anyway) is what is the number to buy such that if you sell them all, you break even?  For that, you set <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x_s\ =\ x_b\">, that is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \frac{x\ +\ 100}{5}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now just solve for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Note that if you only buy that many, the BEST you can do is break even.  Since the general idea of any business venture, whether for profit or for charity, is to make money, you have to buy more than this.  However, this comes with risk.  The more you buy, the more you have to sell in order to turn a profit.  What you really need now is the services of a market research firm that can tell you, within certain statistical limits, what your demand function is.  That is, at any given price point within some sort of reasonable limits, how many candles you can expect to sell.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
document.write( "<div  DISABLED_style= \"text-align:center\"><a  rel=nofollow HREF=\"http://outcampaign.org/\" target=\"_blank\"><IMG STYLE=\"max-width:80%;\" src=\"http://cdn.cloudfiles.mosso.com/c116811/scarlet_A.png\" border=\"0\" alt=\"The Out Campaign: Scarlet Letter of Atheism\" width=\"143\" height=\"122\" /></a></div><BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );