In Troix City, the learning rate is based on a tripling of output instead of the

ID: 469139 • Letter: I

Question

In Troix City, the learning rate is based on a tripling of output instead of the traditional doubling. The first unit of a long production run was produced in 20 hours. In Deux City across the river, the learning rate is based on the usual doubling of output. The first unit of the production run in Deux City took 30 hours. At what level of output will the workers in Deux City become faster than those in Troix City if both locations enjoy an 80% learning rate?

A. 39 units

B. 31 units

C. 35 units

D. 27 units

Explanation / Answer

Tn=T1*n^(lnr/ln2)

where Tn= time to complete nth unit

r=learning rate

n= nth unit

for Troxit City

Tn=T1*n^(ln0.8/ln3)=20*n^(ln0.8/ln3)

T1=20

for Deux City

Tn=T1*n^(ln0.8/ln2)=30*n^(ln0.8/ln2)

T1=30

At nth output Deuxcity becomes faster

hence 30*n^(ln0.8/ln2)<=20*n^(ln0.8/ln3)

hence for n=31 Deux city becomes faster. Deux city takes 9.93 hr and Troxit takes 9.956 hrs

hence option B is the answer

PS-

for Troxit learnig rate is based on tripling

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