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Tooling cost, unit cost and production-volume break-even

Manufacturing alternatives often trade high one-time investment against lower recurring cost.

A simple total-cost model is

$$C(N)=F+cN,$$

where $F$ is fixed tooling/setup investment, $c$ is variable cost per unit and $N$ is production quantity.

Suppose process A needs $F_A=€1{,}000$ and costs $c_A=€20$ per unit, while process B needs $F_B=€25{,}000$ but costs $c_B=€6$ per unit.

The break-even quantity satisfies

$$F_A+c_AN=F_B+c_BN,$$

so

$$N=\frac{25{,}000-1{,}000}{20-6}\approx1714.$$

Below roughly 1714 units, A is cheaper in this simplified model; above it, B is cheaper.

Real decisions also include scrap, cycle time, financing, maintenance, capacity, quality and tooling life, but the model reveals why production volume changes process choice.

A route that requires expensive dedicated tooling can be unattractive for a handful of parts yet economical at large volume. A flexible route with little dedicated tooling can have the opposite cost structure.

Manufacturing economics therefore cannot be separated from process capability: the cheapest feasible route depends on both what the process can make and how many times it must make it.