Final answer:
The Trailblazer Company's break-even point is 5000 units, and they must sell 6050 units to meet a target profit of $73,500. This is calculated using the formulas for break-even and target profit units in cost-volume-profit analysis.
Step-by-step explanation:
To calculate the break-even point in sales units and the number of units required to reach a target profit, we need to apply formulas from cost-volume-profit analysis. We have the selling price per unit, variable cost per unit, and fixed costs for Trailblazer Company.
Total revenue, marginal revenue, total cost, and marginal cost for each output level:
Output Level Total Revenue Marginal Revenue Total Cost Marginal Cost
1 $20 $20 $40 $40
2 $40 $20 $65 $25
3 $60 $20 $100 $35
4 $80 $20 $150 $50
5 $100 $20 $230 $80
The break-even point in units is calculated by the formula:
Break-even units = Fixed costs /(Selling price per unit - Variable cost per unit)
So, for Trailblazer Company:
Break-even units = $350,000 / ($120 - $50)
= $350,000 / $70
= 5000 units
The next part of the question is to find out the number of units needed to achieve a target profit of $73,500. The formula is:
Target profit units = (Fixed costs + Target profit) / (Selling price per unit - Variable cost per unit)
For Trailblazer Company with a target profit of $73,500:
Target profit units = ($350,000 + $73,500) / ($120 - $50)
= $423,500 / $70
= 6050 units
Therefore, the company needs to sell 6050 units to achieve a target profit of $73,500.