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=30×8log2(0.80)T8=30×8log2(0.80) 8=30×80.3219T8=30×80.3219 8=30×0.512T
8=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.