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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?

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Answer:

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