The fifth unit of a long production run was produced in 15 hours.The process has an estimated learning rate of 90 percent.What is the lowest level of output at which the cumulative average production time per unit falls below 15 hours?
A)fewer than or equal to 8 units
B)greater than 8 units but fewer than or equal to 11 units
C)greater than 11 units but fewer than or equal to 14 units
D)greater than 14 units

Question

Quizplus · Accepted Answer

The cumulative average production time per unit can be calculated using the learning curve formula: 
Cumulative Average Production Time = First Unit Time x (Number of Units Produced/Number of Units Produced at 100% Learning Curve)^log(base 2) of Learning Rate

Plug in the given values:
First Unit Time = 15 hours
Learning Rate = 90%
Number of Units Produced at 100% Learning Curve = 1

Cumulative Average Production Time = 15 x (n/1)^log(0.9)

To find the number of units needed to reach a cumulative average production time of less than 15 hours, we can solve for n:

15 x (n/1)^log(0.9) < 15

(n/1)^log(0.9) < 1

n/1 < 1/(log(0.9)(1))

n < 14.4

Therefore, the lowest level of output at which the cumulative average production time per unit falls below 15 hours is 14 units. However, since the question is asking for the "lowest level," we must choose the next lowest option, which is C: greater than 11 units but fewer than or equal to 14 units.

The Fifth Unit of a Long Production Run Was Produced