The weighted-average contribution margin per unit is $36.55. For a $187,000 break-even, 5116 units are needed, with Lens A requiring 1279, Lens B needing 2046, and Lens C requiring 1791 units. To generate a $73,000 profit, 7114 units are needed, distributed among the lenses.
1. Weighted-Average Contribution Margin per Unit:
- Lens A: $38 * 25% = $9.5
- Lens B: $30 * 40% = $12
- Lens C: $43 * 35% = $15.05
- Total Contribution Margin per unit: $9.5 + $12 + $15.05 = $36.55
2. Break-Even Point (Units):
- Break-even point (units) = $187,000 / $36.55 ≈ 5116 units
- Lens A: 5116 * 25% = 1279 units
- Lens B: 5116 * 40% = 2046 units
- Lens C: 5116 * 35% = 1791 units
3. Units to Generate $73,000 Profit:
- Required units = ($187,000 - $73,000) / $36.55 ≈ 7114 units
- Lens A: 7114 * 25% = 1779 units
- Lens B: 7114 * 40% = 2846 units
- Lens C: 7114 * 35% = 2489 units
The complete question is:
Tiago makes three models of camera lens. Its product mix and contribution margin per unit follow: Percentage of Unit sales Contribution Margin per unit Lens A 25 % $ 38 Lens B 40 30 Lens C 35 43 Required: 1. Determine the weighted-average contribution margin per unit. 2. Determine the number of units of each product that Tiago must sell to break even if fixed costs are $187,000. 3. Determine how many units of each product must be sold to generate a profit of $73,000.