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 tenth 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:  Approximately how long will it take to produce the tenth unit?
A)1 hour 
B)2 hours 
C)3 hours 
D)4 hours 
E)5 hours

Quizplus · Accepted Answer

By using the formula y = a*x^b, we can find the equation for the learning curve.

First, we need to find the values of a and b.

Using the data provided, we can choose two points: (1, 5) and (5, 2)

Substituting these points into the formula, we get

5 = a*1^b  (equation 1)
2 = a*5^b  (equation 2)

Dividing equation 1 by equation 2, we get

5/2 = 1/5^b

Taking the logarithm of both sides, we get

log(5/2) = -b*log(5)

Solving for b, we get

b = -log(5/2) / log(5) = 0.4307

Substituting b into equation 1, we get

5 = a*1^0.4307

a = 5 / 1^0.4307 = 8.4

Therefore, the equation for the learning curve is

y = 8.4*x^0.4307

To find the time it takes to produce the tenth unit, we substitute x = 10 into the equation:

y = 8.4*10^0.4307 ≈ 2.98 hours

Therefore, the answer is C) 3 hours.

A Manager Wants to Analyze the Learning Curve Associated with Producing