A manager wants to analyze the learning curve associated with producing one of his company's products. Accordingly, he has gathered the following data: $$\begin{array} { | l | l | }
\hline \text { UNIT PRODUCED } & \text { TIME REQUIRED } \
\hline \text { Second } & 5 \text { hours } \
\hline \text { Fourth } & 4 \text { hours } \
\hline
\end{array}$$
Approximately how long will it take to produce the 10th unit?
A) 1 hour
B) 2 hours
C) 3 hours
D) 4 hours
E) 5 hours

Question

A manager wants to analyze the learning curve associated with producing one of his company's products. Accordingly, he has gathered the following data: $$\begin{array} { | l | l | } 
\hline \text { UNIT PRODUCED } & \text { TIME REQUIRED } \
\hline \text { Second } & 5 \text { hours } \
\hline \text { Fourth } & 4 \text { hours } \
\hline
\end{array}$$
Approximately how long will it take to produce the 10th unit?
A) 1 hour
B) 2 hours
C) 3 hours
D) 4 hours
E) 5 hours

Quizplus · Accepted Answer

We can use the following formula for learning curve:

$T_n=T_1k^n$

where $T_n$ is the time required for n-th unit, $T_1$ is the time required for the first unit, and k is the learning rate.

To find k, we can use the first and fourth units:

$\frac{T_4}{T_1}=(\frac{4}{5})^k$

$k=\frac{\ln(\frac{T_4}{T_1})}{\ln(\frac{4}{5})}\approx0.322$

Using this value of k, we can find the time required for the 10th unit:

$T_{10}=T_1k^{10}=5	imes0.322^{10}\approx3	ext{ hours}$

Therefore, the answer is C.

A Manager Wants to Analyze the Learning Curve Associated with Producing