It took a contractor 1285 hours to manufacture their first unit of an item. If the contractor expects to acheive a 92% unit learning curve, how many hours would be required to manufacture units 51-100/

To determine the hours required to manufacture units 51-100 with a unit learning curve, we need to use the concept of learning curves. The learning curve theory states that as the volume of production doubles, the average hours required to produce one unit decreases by a constant percentage. In this case, we have a 92% learning curve, which means that for every doubling of units produced, the average hours required to produce one unit reduces by 8%.

To find the number of hours required to manufacture units 51-100, we need to determine the cumulative average time per unit at the 100th unit, and then subtract the cumulative average time per unit at the 50th unit. Since the first unit took 1285 hours, we can use it to calculate the cumulative average time per unit at the 100th unit.

First, let's calculate the cumulative average time per unit for the 100th unit using the unit learning curve:

Cumulative average time per unit at the 100th unit = First unit time * (100^(log(learning curve)/log(2)))

Cumulative average time per unit at the 100th unit = 1285 * (100^(log(92%)/log(2)))

Using a calculator:

Cumulative average time per unit at the 100th unit = 1285 * (100^(-0.079181246044317))

Cumulative average time per unit at the 100th unit ≈ 1285 * 0.7390

Cumulative average time per unit at the 100th unit ≈ 950.47 hours (rounded to two decimal places)

Next, we find the cumulative average time per unit at the 50th unit by halving the cumulative average time per unit at the 100th unit:

Cumulative average time per unit at the 50th unit = Cumulative average time per unit at the 100th unit / 2

Cumulative average time per unit at the 50th unit ≈ 950.47 / 2

Cumulative average time per unit at the 50th unit ≈ 475.23 hours (rounded to two decimal places)

Finally, we can find the number of hours required to manufacture units 51-100 by subtracting the cumulative average time per unit at the 50th unit from the cumulative average time per unit at the 100th unit:

Hours required to manufacture units 51-100 ≈ Cumulative average time per unit at the 100th unit - Cumulative average time per unit at the 50th unit

Hours required to manufacture units 51-100 ≈ 950.47 - 475.23

Hours required to manufacture units 51-100 ≈ 475.24 hours (rounded to two decimal places)

Therefore, it would take approximately 475.24 hours to manufacture units 51-100 using the 92% unit learning curve.