A company negotiates a price for two aircraft that includes a reduction in labour on the second aircraft consistent with a 70% learning curve. Suppose the first aircraft took 100 hours. If the improvement rate changes to 20%, how will the total time to complete both aircraft change?
A) no change
B) -10 hours
C) + 10 hours
D) -50 hours
E) + 50 hours

Question

Quizplus · Accepted Answer

Using the learning curve formula, we can find that the second aircraft would take:

Y = aX^b

Where:
- Y = the time required to produce the second aircraft
- X = the cumulative number of units produced
- a = the time required to produce the first unit
- b = the learning rate factor

Using the values given, we have:

100 = a(1)^b
Y = a(2)^b

We are given that the learning rate factor is 70%, so we can calculate a:

a = Y/X^b
a = 100/1^b
a = 100

Next, we can calculate Y for the first scenario (learning rate factor of 70%):

Y = 100(2)^(-0.152)
Y = 71.3 hours

Finally, we can calculate Y for the second scenario (learning rate factor of 20%):

Y = 100(2)^(-0.076)
Y = 85.4 hours

The total time to complete both aircraft is the sum of the time required for each aircraft:

Total time = 100 + 71.3 + 100 + 85.4
Total time = 356.7 hours

Therefore, the change in total time when the learning rate factor changes from 70% to 20% is:

Change in total time = 356.7 - 371.3
Change in total time = +10.0

So the total time will increase by 10 hours. The answer is (C).

A Company Negotiates a Price for Two Aircraft That Includes