document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=72756>Question 72756</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A company has a fixed cost of $75,000. Variable cost per unit is $25. Revenue unit is 75. Find the following:<BR>\n" );
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document.write( "a) Break Even Point<BR>\n" );
document.write( "b) The profit or loss from producing 900 units. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52046 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=52046\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's write two equations. The first equation will be for the Cost (let C represent Cost).<BR>\n" );
document.write( "The Cost is comprised of two parts.  The fixed cost of $75,000 and the variable cost that is <BR>\n" );
document.write( "associated with the production.  That cost is $25 per unit so its cost will be $25 times the<BR>\n" );
document.write( "number of units produced.  Let U represent the number of units produced.  So our cost equation<BR>\n" );
document.write( "is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+25%2AU+%2B+75000 ALIGN=MIDDLE  ALT=\"C+=+25%2AU+%2B+75000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The amount of income or revenue is $75 per unit so that the revenue (call it R) is just the product<BR>\n" );
document.write( "of the income for a single unit times the number of units produced. In equation form this is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R+=+75%2AU ALIGN=MIDDLE  ALT=\"R+=+75%2AU\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The break even point occurs when the revenue (R) just equals the cost C.  We can determine this<BR>\n" );
document.write( "by setting the right side of the cost and revenue equations equal to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75%2AU+=+25%2AU+%2B+75000 ALIGN=MIDDLE  ALT=\"75%2AU+=+25%2AU+%2B+75000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Subtract 25*U from both sides to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50%2AU+=+75000 ALIGN=MIDDLE  ALT=\"50%2AU+=+75000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And solve for U by dividing both sides by 50 to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=U+=+1500 ALIGN=MIDDLE  ALT=\"U+=+1500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "When you produce 1500 units your income just equals your costs.  <BR>\n" );
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document.write( "Another way of looking at this is on a per unit basis.  Since it costs $25 dollars<BR>\n" );
document.write( "to make a unit and you sell units for $75 each, then you are making 50 bucks a unit. And <BR>\n" );
document.write( "you have to sell enough units to offset the $75000 of fixed costs. Therefore you again have<BR>\n" );
document.write( "to divide $50 net income for each unit into the $75000 to find that 1500 units must be<BR>\n" );
document.write( "made and sold to offset the costs.<BR>\n" );
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document.write( "You are also asked to calculate the profit or loss if you make and sell 900 units.<BR>\n" );
document.write( "You can see that it will be a loss because you have to sell 1500 units to break even.<BR>\n" );
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document.write( "For 900 units, the cost is:<BR>\n" );
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document.write( "C 25*900 + 75,000 = 22,500 + 75,000 = $97,500<BR>\n" );
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document.write( "The income meanwhile is:<BR>\n" );
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document.write( "R = 75*900 = $67,500.  <BR>\n" );
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document.write( "The result is that the costs exceed the income by $97,500 - $67,500 = $30,000 so you are out<BR>\n" );
document.write( "$30,000 if you only sell 900 units.<BR>\n" );
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document.write( "Hope this helps you to understand the problem a little better. </SPAN>\n" );
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