document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=537666>Question 537666</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how many widgets must little business inc. make and sell before they start making a profit? Given: total fixed costs are $10,000.00, widgets are sold for $7.50 and the cost to make \"ten\" widgets is $25.00.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #352948 by </B><A HREF=/tutors/aboutme.mpl?userid=lmeeks54><B>lmeeks54(111)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lmeeks54><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=lmeeks54><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=352948\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are a couple of ways to solve this problem.  The easist requires logic and intuition but not much else: there will be a head slapping moment when I explain this.  First let's make sure we know what the question is asking: how many units need to be sold before the business is profitable?  We are asked for the quantity of units at the breakeven point where total costs (normally abbreviated TC) = the total revenues (normally abbreviated TR).<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Total costs (TC) are comprised of fixed costs (FC) + variable costs (VC).  Ignore the fixed costs for a moment (we'll get back to them) and consider the variable costs only.  <BR>\n" );
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document.write( "Given:<BR>\n" );
document.write( "The cost to produce 10 widgets = $25, therefore, divide by 10 to find the VC per widget = $2.50 (at the unit level, this is often called the Marginal Cost (MC), the cost to produce one more unit.)<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Revenue for each widget: $7.50 (like Marginal Cost, this is often called Marginal Revenue (MR), the revenue derived from selling one more unit.)<BR>\n" );
document.write( "...<BR>\n" );
document.write( "We care about the relationship between these two numbers.  The Contribution (towards profits) is the difference between Little Business, Inc.'s (LBI) MR per widget and the MC per widget is: <BR>\n" );
document.write( "MR = $7.50<BR>\n" );
document.write( "MC = $2.50<BR>\n" );
document.write( "Contribution = MR - MC <BR>\n" );
document.write( "= 7.50 - 2.50<BR>\n" );
document.write( "= 5.00 per widget sold<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Now, to get to the breakeven point, LBI must make enough revenue to cover all costs.  At that point, with the next widget sale, they are then making a profit.  <BR>\n" );
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document.write( "Let FC = fixed costs<BR>\n" );
document.write( "Let Qb = quantity of widgets sold at breakeven<BR>\n" );
document.write( "Let P = Price per widget<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Given:<BR>\n" );
document.write( "FC = 10,000<BR>\n" );
document.write( "Calculated:<BR>\n" );
document.write( "Contribution = 5.00<BR>\n" );
document.write( "Need to find:<BR>\n" );
document.write( "Qb<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Short answer to the problem:<BR>\n" );
document.write( "Divide FC by contribution per unit to determine Qb:<BR>\n" );
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document.write( "10,000/5.00 = 2,000 units sold for breakeven<BR>\n" );
document.write( "...<BR>\n" );
document.write( "check your work:<BR>\n" );
document.write( "...<BR>\n" );
document.write( "VC = MC * Qb<BR>\n" );
document.write( "VC = 2.50 * 2,000<BR>\n" );
document.write( "VC = 5,000<BR>\n" );
document.write( "FC = 10,000 (given)<BR>\n" );
document.write( "TC = FC + VC<BR>\n" );
document.write( "TC = 10,000 + 5,000<BR>\n" );
document.write( "TC = 15,000<BR>\n" );
document.write( "...<BR>\n" );
document.write( "TR = P * Qb<BR>\n" );
document.write( "TR = 7.50 * 2,000<BR>\n" );
document.write( "TR = 15,000<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Breakeven occurs where TC = TR<BR>\n" );
document.write( "TR = 15,000<BR>\n" );
document.write( "TC = 15,000<BR>\n" );
document.write( "TC = TR checks<BR>\n" );
document.write( "...<BR>\n" );
document.write( "cheers,<BR>\n" );
document.write( "Lee </SPAN>\n" );
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