Question

Consider a process with a unit cost of $50 for the first unit and a learning rate of 0.9. What will be the unit cost for the 64th unit?

Answer 1

The cumulative average for the learning rate is given by the following formula

Y = ax^b

Y = cumulative average time/cost

a = time/cost for the first unit

x = the number of units

b = log LR/log 2

LR = learning rate in decimals

At 0.9 learning rate the value of b = log 0.9/log 2 = -0.152

This means the cumulative cost to produce 63^rd unit will be

Y1 = 50*63^(-0.152) = 26.63 s

Total cost = 63*26.63 = 1677.69

The cumulative cost to produce 64^th unit will be

Y2 = 50*64^(-0.152) = 26.57

Total cost = 64*26.57 = 1700.48

The cost of producing the 64^th unit will be 1700.48 – 1677.69 = 22.79

Answer 2

To determine the unit cost for the 64th unit using a learning rate of 0.9, we can apply the learning curve formula:

Unit Cost = Initial Unit Cost * (Number of Units)^Learning Rate

Given: Initial Unit Cost = $50 Number of Units = 64 Learning Rate = 0.9

Unit Cost for the 64th unit = $50 * (64^0.9)

Using a calculator or computational tool, we can evaluate this expression:

Unit Cost for the 64th unit = $50 * (64^0.9) ≈ $50 * 19.641 ≈ $982.05

Therefore, the unit cost for the 64th unit, with a learning rate of 0.9, is approximately $982.05.