The first unit of a product took 400 hours to complete. The firm plans to produce 8 units in the first month and 10 units in the second month. If an 80% learning curve is expected, how many hours will the firm use to work on the product during the second month

1,200 hours

Explanation:

Solving mathematically this will be :

y = ax^b

where,

y is the cumulative average time required to produce x units

a is the time required to produce the first unit of output

x is the number of units of output under consideration

b is the log of the Learning Curve % divided by Log 2

The firm use 150 hours to work on the product during the second month

Amount of time used in the first month will be calculated as :

y = 400(8)^(-0.322)

  = 204.8 hours (average)

Total for 8 units = 204.8 hours × 8 units

                           = 1,638.40 hours

Amount of time used for the total months to manufacture 18 units :

y = 400(18)^(-0.322)

  = 157.74 hours (average)

Total for 18 units = 157.74 hours × 18 units

                            = 2,839.32 hours

Therefore,

Hours to be used in the second month = Time on 18 units - Time on 8 units

                                                                 = 2,839.32 hours - 1,638.40 hours

                                                                 = 1,200 hours

So, the firm use 1,200 hours in total for the 10 units. Which gives an average of 120 hours per unit