It takes an employee 30 minutes to produce the first unit of an item.

To calculate the projected time required to produce the eighth unit under an 80% learning curve, we use the learning curve formula. The learning curve indicates that each time production doubles, the time required per unit decreases to 80% of the previous time.

The formula for the learning curve is: ????????=????1×????log⁡????(???????????????????????????????? ????????????????????)Tn​=T1​×nlogb​(learning curve) Where:

????????Tn​ is the time for the nth unit.

????1T1​ is the time for the first unit (30 minutes).

????n is the unit number (8).

????b is the base of the logarithm (2 for doubling).

Learning curve = 0.80.

Using the formula: ????8=30×8log⁡2(0.80)T8​=30×8log2​(0.80) ????8=30×8−0.3219T8​=30×8−0.3219 ????8=30×0.512T8​=30×0.512 ????8=15.36 minutesT8​=15.36 minutes

References:

Chase, R. B., Jacobs, F. R., & Aquilano, N. J. (2006). Operations Management for Competitive Advantage. McGraw-Hill.

Learning curve theory and application articles from professional operations management resources.