A small software company invests $30,000 to produce a software package that will sell for $64.95. Each unit can be produced for $42.25.
How many units must be sold to break even?
How many units must be sold to make a profit of $100,000?
break-even is where cost=revenue. So, you want to solve for x where
42.25x + 30000 = 64.95x
Next, you want
64.95x = 42.25x + 30000 + 100000
To find the number of units that must be sold to break even, we need to calculate the total cost and the revenue per unit.
1. Total cost per unit:
The total cost per unit is the sum of the production cost and the investment cost divided by the number of units produced.
Total cost per unit = (Production cost + Investment cost) / Number of units produced
In this case:
Production cost = $42.25
Investment cost = $30,000
Number of units produced = unknown (let's call it X)
Total cost per unit = ($42.25 + $30,000) / X
2. Revenue per unit:
The revenue per unit is the price at which each unit is sold.
In this case, revenue per unit = $64.95
3. Break-even point:
To break even, the total cost and the total revenue should be equal.
Total cost = Total cost per unit * Number of units produced
Total revenue = Revenue per unit * Number of units produced
Therefore,
Total cost = Total revenue
Total cost per unit * Number of units produced = Revenue per unit * Number of units produced
We can simplify it to:
($42.25 + $30,000) / X * X = $64.95 * X
Now, let's solve for X to find the number of units required to break even.