SOLUTION: 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

Question 537666: 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.

Answer by lmeeks54(111) (Show Source): You can put this solution on YOUR website!
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).
...
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.
...
Given:
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.)
...
Revenue for each widget: $7.50 (like Marginal Cost, this is often called Marginal Revenue (MR), the revenue derived from selling one more unit.)
...
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:
MR = $7.50
MC = $2.50
Contribution = MR - MC
= 7.50 - 2.50
= 5.00 per widget sold
...
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.
...
Let FC = fixed costs
Let Qb = quantity of widgets sold at breakeven
Let P = Price per widget
...
Given:
FC = 10,000
Calculated:
Contribution = 5.00
Need to find:
Qb
...
Short answer to the problem:
Divide FC by contribution per unit to determine Qb:
...
10,000/5.00 = 2,000 units sold for breakeven
...
check your work:
...
VC = MC * Qb
VC = 2.50 * 2,000
VC = 5,000
FC = 10,000 (given)
TC = FC + VC
TC = 10,000 + 5,000
TC = 15,000
...
TR = P * Qb
TR = 7.50 * 2,000
TR = 15,000
...
Breakeven occurs where TC = TR
TR = 15,000
TC = 15,000
TC = TR checks
...
cheers,
Lee
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