A manager wants to analyze the learning curve associated with producing one of his company's products. Accordingly, he has gathered the following data:
Approximately how long will it take to produce the fifth through tenth units?
A) 15 hours
B) 16 hours
C) 18 hours
D) 20 hours
E) 21 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: 
Approximately how long will it take to produce the fifth through tenth units?
A) 15 hours 
B) 16 hours 
C) 18 hours 
D) 20 hours 
E) 21 hours

Quizplus · Accepted Answer

We can use the formula for the learning curve:

y = a * x ^ b

where y is the time per unit, x is the number of units produced, a is the time needed for the first unit, and b is the learning rate.

Using the given data, we can solve for the values of a and b:

2.5 = a * 1 ^ b  (for the first unit)
19 = a * 4 ^ b    (for the fourth unit)

Dividing the second equation by the first, we get:

7.6 = 4 ^ b

Taking the logarithm of both sides, we get:

b = log(7.6) / log(4) ≈ 0.82

Substituting b back into the second equation, we can solve for a:

19 = a * 4 ^ 0.82
a ≈ 39.2

Therefore, the formula for the learning curve is:

y = 39.2 * x ^ 0.82

To find the time needed to produce the fifth through tenth units, we can subtract the time needed for the fourth unit from the time needed for the tenth unit:

y(10) - y(4) = 39.2 * 10 ^ 0.82 - 19 ≈ 20 hours

So the answer is D) 20 hours.

A Manager Wants to Analyze the Learning Curve Associated with Producing