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
To calculate the number of units that need to be sold to break even or make a profit, we need to consider the costs and the selling price.
(a) To break even, the total cost should equal the total revenue. The total cost includes the investment and the production cost of each unit, while the revenue is the selling price multiplied by the number of units sold. Therefore, the equation for break-even is:
Total Cost = Total Revenue
Investment Cost + (Production Cost per Unit * Number of Units) = Selling Price * Number of Units
$30,000 + ($42.25 * Number of Units) = $64.95 * Number of Units
To find the Number of Units required to break even, we can solve this equation.
(b) To calculate the number of units needed to make a profit of $100,000, we add the desired profit to the total cost. Therefore, the equation becomes:
Total Cost + Desired Profit = Total Revenue
$30,000 + ($42.25 * Number of Units) + $100,000 = $64.95 * Number of Units
To find the Number of Units required to make a profit of $100,000, we can solve this equation.
Now, let's solve these equations to find the answers.
(a) How many units must be sold to break even?
$30,000 + ($42.25 * Number of Units) = $64.95 * Number of Units
Simplifying the equation:
$30,000 = $64.95 * Number of Units - $42.25 * Number of Units
$30,000 = $22.70 * Number of Units
Dividing both sides by $22.70:
Number of Units = $30,000 / $22.70
Rounding the answer to the nearest whole number gives us the number of units required to break even.
(b) How many units must be sold to make a profit of $100,000?
$30,000 + ($42.25 * Number of Units) + $100,000 = $64.95 * Number of Units
Simplifying the equation:
$130,000 = $64.95 * Number of Units - $42.25 * Number of Units
$130,000 = $22.70 * Number of Units
Dividing both sides by $22.70:
Number of Units = $130,000 / $22.70
Rounding the answer to the nearest whole number gives us the number of units required to make a profit of $100,000.