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Question 7S.P.2: A manager wants to determine an appropriate learning rate fo......

A manager wants to determine an appropriate learning rate for a new type of work his firm will undertake. He has obtained completion times for the initial six repetitions of a job of this type. What learning rate is appropriate?

Unit Completion Time (hours)
1 15.9
2 12.0
3 10.1
4 9.1
5 8.4
6 7.5
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According to theory, the time per unit decreases at a constant rate each time the output doubles (e.g., unit 1 to 2, 2 to 4, and 3 to 6). The ratios of these observed times will give us an approximate rate. Thus,

\frac{\text{Unit 2}}{\text{Unit 1}}=\frac{12.0}{15.9}=.755 \quad \frac{\text{Unit 4}}{\text{Unit 2}}=\frac{9.1}{12.0}=.758 \quad \frac{\text{Unit 6}}{\text{Unit 3}}=\frac{7.5}{10.1}= .743

Not surprisingly, there is some variability; the rate is usually a smoothed approximation. Even so, the ratios are fairly close—a rate of 75 percent seems reasonable in this case.

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