If it took 1000 hours to produce the first unit of a product, and the learning curve is 80%, how long will it take to produce units 26 through 50?
A) 14,429 hours
B) 7,813 hours
C) 134 hours
D) 3,903 hours
E) 20,122 hours

Question

Quizplus · Accepted Answer

Using the learning curve formula:
Y = aX^b
where:
Y is the time required to produce the Xth unit
a is the time required to produce the first unit
X is the unit number
b is the logarithmic learning rate

To find the time required to produce 26 units:
Y26 = a(26)^b
since we don't know the value of b, we need to find it first,
To do that, we can use the given learning curve percentage, which is 80%.
log(0.8) / log(2) = -0.32193
Therefore, b = -0.32193

Now we can find the time required to produce 26 units:
Y26 = 1000(26)^-0.32193 = 682.77 hours

To find the time to produce 50 units, we use the same formula:
Y50 = a(50)^b

But instead of using 1000 hours as the time required to produce the first unit, we use the time required to produce the 26th unit, which is 682.77 hours.
Y50 = 682.77(50)^-0.32193 = 3912.8 hours

The time to produce units 26 through 50 is the difference between the time to produce the 50th unit and the time to produce the 26th unit:
Y50 - Y26 = 3912.8 - 682.77 = 3229.03 hours, 
rounded to the nearest hour, it is 3,903 hours. Therefore the answer is B.

If It Took 1000 Hours to Produce the First Unit