The direct labor hours required to produce the first two units of a new product are 2,000 and 1,800,respectively.Using a 90% learning rate the company would estimate the direct labor hours for the fifth unit to be
A)1692.4 hours.
B)1620.0 hours.
C)1566.0 hours.
D)1523.2 hours.

Question

The direct labor hours required to produce the first two units of a new product are 2,000 and 1,800,respectively.Using a 90% learning rate the company would estimate the direct labor hours for the fifth unit to be 
A)1692.4 hours.
B)1620.0 hours.
C)1566.0 hours.
D)1523.2 hours.

Quizplus · Accepted Answer

Using the 90% learning rate formula:

𝐿𝑛(𝐻2/𝐻1) = 𝑘𝑛

where:
H1 = hours required for the first unit
H2 = hours required for the second unit
k = learning curve coefficient

We solve for k first:

k = 𝐿𝑛(𝐻2/𝐻1) / 𝐿𝑛(2)

k = 𝐿𝑛(1,800/2,000) / 𝐿𝑛(2)
k = -0.152

Then for the fifth unit, we use this formula:

H5 = H1 * (5^k)

H5 = 2,000 * (5^-0.152)
H5 = 1,566 hours

Therefore, the estimated direct labor hours for the fifth unit is 1,566 hours. The best choice is C.

The Direct Labor Hours Required to Produce the First Two