The first unit of production takes 20 hours to produce and the learning rate is expected to be 90 percent. how long will it take to produce the twelfth unit? less than or equal to 11.0 hours greater than 11.0 hours but less than or equal to 13.0 hours greater than 13.0 but less than or equal to 15.0 hours greater than 15.0 hours

Question

Mathematics

Yael

24 July, 03:35

The first unit of production takes 20 hours to produce and the learning rate is expected to be 90 percent. how long will it take to produce the twelfth unit? less than or equal to 11.0 hours greater than 11.0 hours but less than or equal to 13.0 hours greater than 13.0 but less than or equal to 15.0 hours greater than 15.0 hours

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Sylvia Byrd · Answer 1

Learning curve rate, r, means the ratio of production time satisfies the relation

T_2k=r*T_k

solving the equation gives

T (n) = (T_initial) * (n^b) where b=log (r) / log (2)

Here, r=0.9 = > b=log (0.9) / log (2) = - 0.15200

n=12, T_initial=20

=>

T (12) = 20*12^ (-0.15200) = 13.71 hours