Question

If the tenth unit produced took 24 hours and the fifth unit took 32 hours, answer the following. a) What is the learning rate? b) How long did the first unit take to complete? c) How long did the third unit take to complete?

Answer 1

Given time taken for 10th unit = 24 hours

T10 = T*(10)^b

Where b = ln(P) /ln(2)

And T is the time taken to produce 1st unit

Where P is the learning rate.

Similarly time taken for 5th unit = 32 hours

T5 = T*(5)^b

Dividing T10 and T5

24/32 = 10^b/5^b

2^b = 0.75

b = ln(0.75)/ln(2)

ln(p)/ln(2) = ln(0.75)/ln(2)

Therefore P = 0.75

Question A. Learning rate = 0.75 or 75%

b = - 0.415

T = T10 / (10^b)

= 24/(10^-0.415)

= 62.40

Question B. It takes 62.40 hours to produce first unit.

Question C.

T3 = T*(3^b)

= 62.40* (3^-0.415)

= 39. 55

So it takes 39.55 hours to produce 3rd unit

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