Question 459575: 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.
Answer by math-vortex(648)   (Show Source):
You can put this solution on YOUR website! 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.
Let
n = number of units sold
I = income from selling n units
E = expenses for selling n units
We need two equations--one for income, one for expense--in terms of n
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INCOME is the number of units Davis sold times the selling price
I = 20n
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EXPENSES are the fixed costs plus the number of units Davis sold times the unit cost
E = 600,000 + 15n
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We want to know when income exceeds expenses. Here's how we say that mathematically:
I > E
.
Now it's a simple matter of substituting the equivalent expressions we have for I and E. We get
20n > 6000,000 + 15n
'
Solve for n to find the appropriate values for n
20n - 15n > 500,000
5n > 600,000
n > 120,000
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.
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CHECK
It's always a good idea to check our answers. Substitute 120,000 for n in the income and expense equations.
I = 20n = 20(120,000) = 2,400,000
E = 600,000 + 15n = 600,000 + 15(120,000) = 2,400,000
We see that when Davis sells exactly 120,000 units, income and expense are equal. This is the break even point.
.
However, if Davis sells 120,001 units, look what happens:
I = 20(120,010) = 2,400,020
E = 600,000 + 15(120,001) = 2,400,015
The income is $5 more than the expenses. The Davis Company has made a profit.
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