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Break-even between production methods

Different production methods have different cost structures: 3D printing has low or no start-up cost but high cost per part, while injection molding has an expensive mold as a fixed cost but low cost per part. The break-even quantity is where the two methods cost exactly the same.

Q0⋅k1=F2+Q0⋅k2Q_0\cdot k_1 = F_2 + Q_0\cdot k_2total cost is equal at the break-even quantity Q0Q_0

Symbols

k1k_1cost per part, method with no fixed cost (e.g. 3D printing)kr
F2F_2fixed cost of method 2 (e.g. mold)kr
k2k_2cost per part, method 2kr

Example

3D printing 100 kr/unit. Injection molding: mold 20,000 kr + 10 kr/unit.

100Q=20000+10Q⇒Q=20000/90≈222100Q = 20000 + 10Q \Rightarrow Q = 20000/90 \approx 222 units.

Below the break-even quantity, the method with low fixed cost is cheapest; above it, the opposite is true.
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