Calculate the rate of learning at which the initial production phase profit target would be achieved, assuming no other cost savings can be made.
Assuming no other cost savings can be made the direct labour cost would have to reduce by $1,903 (i.e. the excess of cost above the target cost) to a total cost of $6,600 which is the equivalent of 660 hours at $10 per hour.
660 hours in total represents an average time of 10.3125 hours per batch (660 / 64 batches)
Since the learning continued throughout the production of the 64 batches then this average can be used to determine the rate of learning required to achieve the target variable cost.
64 batches of production represent 6 doublings of cumulative output therefore:
10.3125 / 25 = 0.4125
6√0.4125 = 0.8628
The learning rate at which the target variable cost would be achieved is 86.3%