An operations manager observes a new production process. Based on production of the first 32 units, the manager estimates that the learning rate is 85 %. If unit #32 took 23.52 minutes to complete and the manger is correct about the learning rate, how long will unit #128 take to complete?

The answer is 17.01 minutes

Explanation:

Given that:

The learning rate (r) = 85% = 0.85

T₃₂ = 23.52 minutes

By applying the learning curve formula

Thus,

Tₙ = T₁ nᵇ

Where b represent ln (r) / ln2

b = ln (0.85) / ln2 = - 0.2344

23.55 = T₁ * (32) ^-0.2344

T₁ = 23.55 * (32) ^0.2344

Now,

T₁₂₈ = T₁ (128) ^ - 0.2344

= 23.55 * (32) ^0.2344 * (128) ^ - 0.2344

=17.01 minutes