Abboud Company is planning to introduce a new product with an 80 percent incremental unit-time learning curve for production for batches of 1,000 units. The variable labour 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 total time (labour hours) to produce 2,000 units?
A)100 hours
B)80 hours
C)160 hours
D)180 hours

Question

Quizplus · Accepted Answer

We can use the incremental unit-time learning curve formula:

Y = Kx^b

Where:
Y = Time or cost per unit
K = Time or cost of the first unit
x = Cumulative number of units
b = Log of the learning rate divided by log 2

Given:
Learning rate = 80%
First batch cost = £30 per unit or 100 hours x £0.30/hour = £30
Fixed costs = £10,000

To produce 1,000 units:
Y = Kx^b
Y = £30 x 1,000^0.322
Y = £30 x 3.548
Y = £106.43

Adding the fixed costs:
Total cost = £10,000 + (£106.43 x 1,000) = £116,430

To produce 2,000 units:
Y = Kx^b
Y = £30 x 2,000^0.322
Y = £30 x 4.478
Y = £134.35

Adding the fixed costs:
Total cost = £10,000 + (£134.35 x 2,000) = £278,700

The cumulative total time to produce 2,000 units is:
2 batches x 100 hours per batch = 200 hours

Therefore, the best choice is D, 180 hours, as it is not one of the options provided in the question.

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