Question

Company Q plans to make a new product next year and sell each unit of this new product at a selling price of 2. The variable costs per unit in each production run are estimated to be 40% of the selling price, and the fixed costs for each production run are estimated to be $5,040. Based on these estimated costs, how many units of the new product will Company Q need to make and sell in order for their revenue to equal their total costs for each production run?

Hint:

To calculate the break-even point, set the revenue equal to the total costs and solve for the number of units.

Answer 1

Step 1: Define the variables. 
Let \( x \) be the number of units that Company Q needs to sell. 
Step 2: Calculate the revenue. 
Revenue is given by: \[ \text{Revenue} = \text{Selling price} \times \text{Number of units sold} = 2x \] Step 3: Calculate the total costs. 
The total cost is the sum of the fixed costs and the variable costs. The variable cost per unit is 40% of the selling price, i.e.: \[ \text{Variable cost per unit} = 0.4 \times 2 = 0.8 \] Thus, the total variable cost for \( x \) units is: \[ \text{Total variable cost} = 0.8x \] The total cost is the sum of the fixed cost and the variable cost: \[ \text{Total cost} = 5040 + 0.8x \] Step 4: Set up the equation for break-even point. 
At the break-even point, the revenue equals the total costs: \[ 2x = 5040 + 0.8x \] Step 5: Solve for \( x \). 
Subtract \( 0.8x \) from both sides: \[ 2x - 0.8x = 5040 \] \[ 1.2x = 5040 \] Solve for \( x \): \[ x = \frac{5040}{1.2} = 4200 \] Step 6: Conclusion. 
Thus, Company Q needs to make and sell 4,200 units of the new product in order to break even.