Question

Question #1: Wall, Corp. (Wall) is the leading manufacturer of drywall in the United States. Dry, Inc. (Dry) has announced plans to begin selling a new and improved type of drywall starting next year. To maintain their position as the leading manufacturer, and to compete with Dry, Wall decided to start producing an improved type of drywall as well. When the production line started, it took 29 hours to make the first batch of 100 8' by 4' sheets. Wall estimates the learning rate to be 75%. Forecasting the cumulative average time per batch to make the first seven batches of 8' by 4' sheets, and using that average, what is the total production hours to make these seven batches of sheets?

QUESTION #2
A company implements a new process to manufacture its product and spends $400 on labor to produce one batch. It expects that the new process will be subject to a 70% learning curve. If the company assumes the learning curve will follow the cumulative average-time learning model, what will be the total labor cost to produce 200 units if each batch is 100 units?

QUESTION #3
A company implements a new process to manufacture its product and spends $500 on labor to produce 50 units. It expects that the new process will be subject to an 80% learning curve. If the company assumes the learning curve will follow the cumulative average-time learning model, what will be the total labor cost to produce 200 units?

Answer 1

The answer to the first question:

Question # 1. This problem can be solved by the following formula:

Y=a(X)^b

Where,

Y = Cumulative average time per batch

X=Cumulative number of batch need to be produced =7

a = Time taken in the production of first batch = 29 hours

b= log of the learning rate (0.75)/ Log of 2 =

= -0.124938737/.3010

=-0.41504

Therefore, Y = 29*((7)^(-0.41504)) = 12.93 hour per batch as cumulative average

Total time of production for 7 batch = 12.93*7= 90.52 hours.