Figure 3-9
Hereford Company is planning to introduce a new product with an 80 percent learning rate for production for batches of 1,000 units. The variable labor costs are $30 per unit for the first 1,000-unit batch. Each batch requires 100 hours. There are $10,000 in fixed costs not subject to learning.
-Refer to Figure 3-9. What is the cumulative average time per batch using the incremental unit-time learning curve for 2,000 units?
A) 180
B) 100
C) 90
D) 80

Question

Quizplus · Accepted Answer

Using the incremental unit-time learning curve, we can calculate the cumulative average time per batch as follows:

For the first 1,000 units:
Cumulative average time per batch = (100 hours/ 1) = 100 hours/batch

For the second 1,000 units:
Learning rate = 80%
Cumulative average time for the first batch of the second 1,000 units = 100 hours
Cumulative average time for the second batch of the second 1,000 units = 100 * 0.8 = 80 hours
Cumulative average time for the third batch of the second 1,000 units = 80 * 0.8 = 64 hours
Cumulative average time for the fourth batch of the second 1,000 units = 64 * 0.8 = 51.2 hours
Cumulative average time for the fifth batch of the second 1,000 units = 51.2 * 0.8 = 40.96 hours
Cumulative average time for the sixth batch of the second 1,000 units = 40.96 * 0.8 = 32.768 hours
Cumulative average time for the seventh batch of the second 1,000 units = 32.768 * 0.8 = 26.2144 hours
Cumulative average time for the eighth batch of the second 1,000 units = 26.2144 * 0.8 = 20.97152 hours

Therefore, the cumulative average time per batch for 2,000 units using the incremental unit-time learning curve is:

(100 + 100 + 80 + 64 + 51.2 + 40.96 + 32.768 + 26.2144 + 20.97152) / 9
= 90.02 hours/batch (rounded to two decimal places)

So, the best choice is C.

Figure 3-9 Hereford Company Is Planning to Introduce a New Product with Product