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. What is the cumulative average time per batch using the incremental unit-time learning curve for 2,000 units?

Question

Quizplus · Accepted Answer

The incremental unit-time learning curve formula is:
Tn = T1 * n^log(r) where T1 = initial time per unit, n = cumulative number of units produced, and r = learning rate.

For the first batch of 1,000 units:
T1 = 100 hours / 1,000 units = 0.1 hours per unit
r = 80% = 0.8
T1000 = 0.1 * 1,000^log(0.8) = 0.1 * 43.426 = 4.343 hours per unit

For the second batch of 1,000 units:
T2000 = 0.1 * 2,000^log(0.8) = 0.1 * 34.133 = 3.4133 hours per unit

The cumulative average time per batch for 2,000 units is the total time for 2,000 units divided by the number of batches, which is:
(1,000 units * 4.343 hours per unit + 1,000 units * 3.4133 hours per unit) / 2,000 units = 0.0378685 hours per unit * 60 minutes per hour = 2.27211 minutes per unit
Rounding to the nearest minute, the answer is 90 minutes per batch (2.27211 * 40 units per batch). Therefore, the best choice is (C) 90.

Hereford Company Is Planning to Introduce a New Product with an 80