document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=459575>Question 459575</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this problem. The Davis Company manufactures a product that has a unit selling price of $20 and a unit cost of $15. If fixed costs are $600,000 , determine the least number of units that must be sold for the company to have a profit. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #315139 by </B><A HREF=/tutors/aboutme.mpl?userid=math-vortex><B>math-vortex(648)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math-vortex><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=math-vortex><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=315139\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The big idea we will use to solve this problem is that the Davis Company will make a profit when their income exceeds their expenses.\r<BR>\n" );
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document.write( "Let<BR>\n" );
document.write( "n = number of units sold<BR>\n" );
document.write( "I = income from selling n units<BR>\n" );
document.write( "E = expenses for selling n units\r<BR>\n" );
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document.write( "We need two equations--one for income, one for expense--in terms of n\r<BR>\n" );
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document.write( "---<BR>\n" );
document.write( "INCOME is the number of units Davis sold times the selling price<BR>\n" );
document.write( "I = 20n<BR>\n" );
document.write( "---<BR>\n" );
document.write( "EXPENSES are the fixed costs plus the number of units Davis sold times the unit cost<BR>\n" );
document.write( "E = 600,000 + 15n<BR>\n" );
document.write( "---<BR>\n" );
document.write( "We want to know when income exceeds expenses. Here's how we say that mathematically:<BR>\n" );
document.write( "I > E<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now it's a simple matter of substituting the equivalent expressions we have for I and E. We get<BR>\n" );
document.write( "20n > 6000,000 + 15n<BR>\n" );
document.write( "'<BR>\n" );
document.write( "Solve for n to find the appropriate values for n<BR>\n" );
document.write( "20n - 15n > 500,000<BR>\n" );
document.write( "5n > 600,000<BR>\n" );
document.write( "n > 120,000\r<BR>\n" );
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document.write( "We interpret this to mean that when n > 120,000, the income will exceed expenses. So, 120,001 is the least number of units Davis must sell to make a profit.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "CHECK<BR>\n" );
document.write( "It's always a good idea to check our answers. Substitute 120,000 for n in the income and expense equations.<BR>\n" );
document.write( "I = 20n = 20(120,000) = 2,400,000<BR>\n" );
document.write( "E = 600,000 + 15n = 600,000 + 15(120,000) = 2,400,000\r<BR>\n" );
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document.write( "We see that when Davis sells exactly 120,000 units, income and expense are equal. This is the break even point.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "However, if Davis sells 120,001 units, look what happens:<BR>\n" );
document.write( "I = 20(120,010) = 2,400,020<BR>\n" );
document.write( "E = 600,000 + 15(120,001) = 2,400,015\r<BR>\n" );
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document.write( "The income is $5 more than the expenses. The Davis Company has made a profit.<BR>\n" );
document.write( " </SPAN>\n" );
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