In the following discussion and applications, we focus on direct labor hours per unit, although we could as easily have used costs. When we develop a learning curve, we make the following assumptions:

The direct labor required to produce the $n+1$ unit will always be less than the direct labor required for the

`n`th unit.Direct labor requirements will decrease at a declining rate as cumulative production increases.

The reduction in time will follow an exponential curve.

In other words, the production time per unit is reduced by a fixed percentage each time production is doubled. We can use a logarithmic model to draw a learning curve. The direct labor required for the `n`th unit, ${k}_{n},$ is

$${k}_{n}={k}_{1}{n}^{b}$$

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