Sk8Lab is a business that manufactures and sells skateboards. The business has provided the following information:

Product Sales Price Variable Cost Sales mix
Street skateboards 200 97 4
Long skateboards 150 65 1
Cruiser skateboards 95 35 3

Fixed costs are $12,500.

How many skateboards in total need to be sold to break even? Please answer in whole units

Question

Sk8Lab is a business that manufactures and sells skateboards. The business has provided the following information:

Product	Sales Price	Variable Cost	Sales mix
Street skateboards	200	97	4
Long skateboards	150	65	1
Cruiser skateboards	95	35	3

Fixed costs are $12,500.

How many skateboards in total need to be sold to break even? Please answer in whole units

BlackTom AI · Accepted Answer

Using the weighted-average contribution margin per unit for a multi-product firm gives the correct break-even in units.

1) Relevant knowledge points and concepts
- Contribution margin per unit = Sales price − Variable cost.
- For multiple products sold in a sales mix, compute the total contribution for one complete mix, then divide by total units in that mix to get the weighted-average contribution per unit.
- Break-even units (in the mix) = Fixed costs ÷ Weighted-average contribution per unit. Because units must be whole, round up to the next whole unit.

2) Step-by-step reasoning
- Compute contribution margin for each product.
- Apply sales-mix weights to get total contribution from one full mix.
- Find average contribution per unit = (total contribution of mix) ÷ (total units in mix).
- Divide fixed costs by that average contribution per unit to get break-even units; round up.

3) Calculations with intermediate steps
- Contribution margins:
  Street = 200 − 97 = 103
  Long = 150 − 65 = 85
  Cruiser = 95 − 35 = 60
- Sales mix quantities: Street 4, Long 1, Cruiser 3 → total units per mix = 4 + 1 + 3 = 8
- Total contribution per full mix = 4×103 + 1×85 + 3×60
  = 412 + 85 + 180
  = 677
- Weighted-average contribution per unit = 677 ÷ 8 = 84.625
- Break-even units = Fixed costs ÷ average contribution = 12,500 ÷ 84.625
  Note 84.625 = 677/8, so 12,500 ÷ (677/8) = 12,500×8/677 = 100,000/677 ≈ 147.7106
- Because partial units cannot be sold, round up: 148 units.

4) Why the correct answer is correct
Selling 148 boards at the given sales mix yields total contribution ≥ fixed costs. At 147 units the total contribution is 147 × 84.625 = 12,439.875 which is less than fixed costs ($12,500). At 148 units the contribution is 148 × 84.625 = 12,524.5, which covers fixed costs and reaches break-even. Therefore 148 whole units are required.

5) Other options
- Not applicable (this is a numerical question). Any smaller whole-unit answer (e.g., 147) would leave contribution short of fixed costs; any larger answer would still cover fixed costs but is not the minimum break-even.

6) Conclusion
The minimum total number of skateboards that must be sold to break even, given the provided sales mix and costs, is 148 units, which matches the provided answer.

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