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. (Round your answers to the nearest whole number.)
(a) How many units must be sold to break even?
units
(b) How many units must be sold to make a profit of $100,000?
units
cost = 30,000 + 42.25 x
so
64.95 x = 30,000 + 42.25 x
profit = (64.95-421.25)x - 30,000 = 100,000
To find the answers to these questions, we need to calculate the break-even point and the number of units required to make a specific profit.
(a) To determine the break-even point, we need to calculate the total cost and the revenue:
Total Cost = Fixed Costs + Variable Costs
Fixed Costs = $30,000
Variable Costs per unit = $42.25
Revenue = Selling Price per unit * Number of units
Selling Price per unit = $64.95
Let's calculate the break-even point by equating the total cost and revenue:
Total Cost = Revenue
$30,000 + ($42.25 * Number of units) = $64.95 * Number of units
Simplifying the equation, we get:
$30,000 + $42.25 * Number of units = $64.95 * Number of units
$30,000 = $22.7 * Number of units
Number of units = $30,000 / $22.7
Now, let's calculate the value of the number of units:
Number of units = 30,000 / 22.7
Number of units = 1320
Hence, to break even, the company needs to sell approximately 1,320 units.
(b) To find the number of units needed to make a profit of $100,000, we will use a similar approach:
Profit = Revenue - Total Cost
Total Cost = $30,000 + ($42.25 * Number of units)
Revenue = $64.95 * Number of units
Set the equation as follows:
$100,000 = ($64.95 * Number of units) - ($30,000 + ($42.25 * Number of units))
Now, solve for the number of units:
$100,000 = $64.95N - $30,000 - $42.25N
$100,000 + $30,000 = $64.95N - $42.25N
$130,000 = $22.7N
To find the value of N:
N = $130,000 / $22.7
Now calculate the value of N:
N = 130000 / 22.7
N ≈ 5725
Therefore, approximately 5725 units will need to be sold to make a profit of $100,000.