Conversion Factors for the Cumulative Average Number of Direct Labor Hours per Unit
\(\begin{array}{c}
\begin{array}{c}
80 \% \text { Learning Rate }\
\text { ( } n=\text { cumulative production) }\
\begin{array}{rrrrrr}
\hline n & & n & & {n} & \
\hline 1 & 1.00000 & 19 & 0.53718 & 37 & 0.43976 \
2 & 0.90000 & 20 & 0.52425 & 38 & 0.43634 \
3 & 0.83403 & 21 & 0.51715 & 39 & 0.43304 \
4 & 0.78553 & 22 & 0.51045 & 40 & 0.42984 \
5 & 0.74755 & 23 & 0.50410 & 64 & 0.37382 \
6 & 0.71657 & 24 & 0.49808 & 128 & 0.30269 \
7 & 0.69056 & 25 & 0.49234 & 256 & 0.24405 \
8 & 0.66824 & 26 & 0.48688 & 512 & 0.19622 \
9 & 0.64876 & 27 & 0.48167 & 600 & 0.18661 \
10 & 0.63154 & 28 & 0.47668 & 700 & 0.17771 \
11 & 0.61613 & 29 & 0.47191 & 800 & 0.17034 \
12 & 0.60224 & 30 & 0.46733 & 900 & 0.16408 \
13 & 0.58960 & 31 & 0.46293 & 1,000 & 0.15867 \
14 & 0.57802 & 32 & 0.45871 & 1,200 & 0.14972 \
15 & 0.56737 & 33 & 0.46464 & 1,400 & 0.14254 \
16 & 0.55751 & 34 & 0.45072 & 1,600 & 0.13660 \
17 & 0.54834 & 35 & 0.44694 & 1,800 & 0.13155\
18& 0.53979 & 36 & 0.44329 & 2,000 & 0.12720
\end{array}
\end{array}
\begin{array}{cl}
90 \% \text { Learning Rate }\
\text { ( } n=\text { cumulative production) }\
\begin{array}{rrrrrr}
\hline n &&{n} & &n & \
\hline 1 & 1.00000 & 19 & 0.73545 & 37 & 0.67091 \
2 & 0.95000 & 20 & 0.73039 & 38 & 0.66839 \
3 & 0.91540 & 21 & 0.72559 & 39 & 0.66595 \
4 & 0.88905 & 22 & 0.72102 & 40 & 0.66357 \
5 & 0.86784 & 23 & 0.71666 & 64 & 0.62043 \
6 & 0.85013 & 24 & 0.71251 & 128 & 0.56069 \
7 & 0.83496 & 25 & 0.70853 & 256 & 0.50586 \
8 & 0.82172 & 26 & 0.70472 & 512 & 0.45594 \
9 & 0.80998 & 27 & 0.70106 & 600 & 0.44519 \
10 & 0.79945 & 28 & 0.69754 & 700 & 0.43496 \
11 & 0.78991 & 29 & 0.69416 & 800 & 0.42629 \
12 & 0.78120 & 30 & 0.69090 & 900 & 0.41878 \
13 & 0.77320 & 31 & 0.68775 & 1,000 & 0.41217 \
14 & 0.76580 & 32 & 0.67471 & 1,200 & 0.40097 \
15 & 0.75891 & 33 & 0.68177 & 1,400 & 0.39173 \
16 & 0.75249 & 34 & 0.67893 & 1,600 & 0.38390 \
17 & 0.74646 & 35 & 0.67617 & 1,800 & 0.37711 \
18 & 0.74080 & 36 & 0.67350 & 2,000 & 0.37114
\end{array}
\end{array}
\end{array}\)

-The fifth unit of a long production run was produced in 15 hours.The process has an estimated learning rate of 90 percent.What is the lowest level of output at which the average production time per unit falls below 15 hours? Refer to the copy of Table G.1 above.
A) Fewer than or equal to 8 units
B) Greater than 8 units but fewer than or equal to 11 units
C) Greater than 11 units but fewer than or equal to 14 units
D) Greater than 14 units

Question

Conversion Factors for the Cumulative Average Number of Direct Labor Hours per Unit
\(\begin{array}{c}
\begin{array}{c}
80 \% \text { Learning Rate }\
\text { ( } n=\text { cumulative production) }\
\begin{array}{rrrrrr}
\hline n & & n & & {n} & \
\hline 1 & 1.00000 & 19 & 0.53718 & 37 & 0.43976 \
2 & 0.90000 & 20 & 0.52425 & 38 & 0.43634 \
3 & 0.83403 & 21 & 0.51715 & 39 & 0.43304 \
4 & 0.78553 & 22 & 0.51045 & 40 & 0.42984 \
5 & 0.74755 & 23 & 0.50410 & 64 & 0.37382 \
6 & 0.71657 & 24 & 0.49808 & 128 & 0.30269 \
7 & 0.69056 & 25 & 0.49234 & 256 & 0.24405 \
8 & 0.66824 & 26 & 0.48688 & 512 & 0.19622 \
9 & 0.64876 & 27 & 0.48167 & 600 & 0.18661 \
10 & 0.63154 & 28 & 0.47668 & 700 & 0.17771 \
11 & 0.61613 & 29 & 0.47191 & 800 & 0.17034 \
12 & 0.60224 & 30 & 0.46733 & 900 & 0.16408 \
13 & 0.58960 & 31 & 0.46293 & 1,000 & 0.15867 \
14 & 0.57802 & 32 & 0.45871 & 1,200 & 0.14972 \
15 & 0.56737 & 33 & 0.46464 & 1,400 & 0.14254 \
16 & 0.55751 & 34 & 0.45072 & 1,600 & 0.13660 \
17 & 0.54834 & 35 & 0.44694 & 1,800 & 0.13155\
18& 0.53979 & 36 & 0.44329 & 2,000 & 0.12720
\end{array}
\end{array}
\begin{array}{cl}
90 \% \text { Learning Rate }\
\text { ( } n=\text { cumulative production) }\
\begin{array}{rrrrrr}
\hline n &&{n} & &n & \
\hline 1 & 1.00000 & 19 & 0.73545 & 37 & 0.67091 \
2 & 0.95000 & 20 & 0.73039 & 38 & 0.66839 \
3 & 0.91540 & 21 & 0.72559 & 39 & 0.66595 \
4 & 0.88905 & 22 & 0.72102 & 40 & 0.66357 \
5 & 0.86784 & 23 & 0.71666 & 64 & 0.62043 \
6 & 0.85013 & 24 & 0.71251 & 128 & 0.56069 \
7 & 0.83496 & 25 & 0.70853 & 256 & 0.50586 \
8 & 0.82172 & 26 & 0.70472 & 512 & 0.45594 \
9 & 0.80998 & 27 & 0.70106 & 600 & 0.44519 \
10 & 0.79945 & 28 & 0.69754 & 700 & 0.43496 \
11 & 0.78991 & 29 & 0.69416 & 800 & 0.42629 \
12 & 0.78120 & 30 & 0.69090 & 900 & 0.41878 \
13 & 0.77320 & 31 & 0.68775 & 1,000 & 0.41217 \
14 & 0.76580 & 32 & 0.67471 & 1,200 & 0.40097 \
15 & 0.75891 & 33 & 0.68177 & 1,400 & 0.39173 \
16 & 0.75249 & 34 & 0.67893 & 1,600 & 0.38390 \
17 & 0.74646 & 35 & 0.67617 & 1,800 & 0.37711 \
18 & 0.74080 & 36 & 0.67350 & 2,000 & 0.37114
\end{array}
\end{array}
\end{array}\)

-The fifth unit of a long production run was produced in 15 hours.The process has an estimated learning rate of 90 percent.What is the lowest level of output at which the average production time per unit falls below 15 hours? Refer to the copy of Table G.1 above.
A) Fewer than or equal to 8 units
B) Greater than 8 units but fewer than or equal to 11 units
C) Greater than 11 units but fewer than or equal to 14 units
D) Greater than 14 units

Quizplus · Accepted Answer

Using the data from the table for 90% learning rate, we can find the cumulative average number of direct labor hours per unit after producing the 5th unit.

For the 5th unit, the time taken is 15 hours, so the cumulative number of direct labor hours for the first 5 units is 1+1+0.9154+0.88905+0.86784=4.67229 hours.

Using the conversion factor for cumulative average number of direct labor hours per unit:

$n=5$ has a conversion factor of 0.71651
$n=6$ has a conversion factor of 0.70013
$n=7$ has a conversion factor of 0.68455
$n=8$ has a conversion factor of 0.66969
$n=9$ has a conversion factor of 0.65549

Multiplying the cumulative average number of direct labor hours per unit by the cumulative number of direct labor hours for the first 5 units, we get the cumulative number of direct labor hours for each of the next units:

$n=5$ has a cumulative number of direct labor hours of 4.67229
$n=6$ has a cumulative number of direct labor hours of $4.67229 	imes 0.71651 = 3.34998$
$n=7$ has a cumulative number of direct labor hours of $4.67229 	imes 0.71651 	imes 0.70013 = 2.34627$
$n=8$ has a cumulative number of direct labor hours of $4.67229 	imes 0.71651 	imes 0.70013 	imes 0.68455 = 1.60367$
$n=9$ has a cumulative number of direct labor hours of $4.67229 	imes 0.71651 	imes 0.70013 	imes 0.68455 	imes 0.66969 = 1.05393$

We can see that the cumulative number of direct labor hours per unit falls below 15 hours for the first time at $n=14$. Therefore, the lowest level of output at which the average production time per unit falls below 15 hours is greater than 11 units but fewer than or equal to 14 units. So the answer is C.