Question

Question Help The cumulative average labor hours to assemble the first five units of product A was 15.962 hours. If the learning curve, based on the previous experience with similar products, is 85%, what is the estimated time (labor hours) that will be required to assemble the 21" unit? The number of labor hours required to assemble the 21th unit is hours. (Round to one decimal place.) Enter your answer in the answer box and then click Check Answer. All parts showing Clear All Check Answer Previous Next ORA 9:25 AM + (0) 0/16/2019 0 D

Answer 1

1.9393 hours

Explanation:

In general, if the learning curve is p%, then the time
`\bf T_n` estimated to produce the nth unit is given by the logarithmic curve

`\bf T_n=T_1n^b`

where

`\bf T_1` is the time needed to produce unit 1

and b is given by

`\bf b=(log(p/100))/(log(2))` (slope of the learning curve)

In our case

`\bf T_n=T_1n^(log(0.85)/log(2))=T_1n^((-0.2344))`

So we must find
`\bf T_1`

We know that the cumulative average labor hours to assemble the first five units of product A was 15.962 hours, hence

`\bf T_1+T_2+T_3+T_4+T_5=15.962`

applying the formula,

`\bf T_1+T_12^((-0.2344))+T_13^((-0.2344))+T_14^((-0.2344))+T_15^((-0.2344))=15.962`

factorizing

`\bf T_1(1+2^((-0.2344))+3^((-0.2344))+4^((-0.2344))+5^((-0.2344)))=15.962`

computing the terms we have

`\bf T_1(4.0311)=15.962\rightarrow T_1=3.9597\;hours`

Finally, to compute the time estimated to produce the 21st unit, we replace in the formula with n=21

`\bf \boxed{T_(21)=3.9597(21)^(-0.2344)=1.9393\;hours}`