Question

Bachmann Products, Inc., has found that new products follow a learning curve. The first two units have been completed with the following results:

Units Produced	Marginal Labor Time
1	80.00
2	56.00

How much time will be needed to complete the 8^th unit?

62.00 hours.

39.20 hours.

32.00 hours.

27.44 hours.

Answer 1

The Answer of this question can be simply given through formula but I have explained knowingly it much lengthy to get conceptual clarity...

The learning curve is based on doubling of production

The first unit takes time of 80 hours. i.e when production doubles decrease in time per unit affect the rate of learning curve.

Time required for (N)^th unit = T × L^{​​​​​​n}

^{where T= Unit time of 1st unit. L = Learning curve rate. n = No of times T is doubled.}

^​​​​since, 1st unit takes 80 hours

It's double is second unit takes 56 hours

Applying the formula , Time required for 2nd unit = 1st unit time × L^{​​​​​n.}

  i.e. 56 = 80 × L^{​​​​​​1}

Therefore, Learning rate (L) = 70% i.e. 0.7

Since we know each time when the production doubles, labor per unit declines by a constant factor, known as the learning rate.

Accordingly as the unit doubles to 4 units then 8 units the time taken in hours to complete the product to be declined or reduced to 70% of earlier time taken.

Hence the time taken for 4th unit will be 70% of 56 hours ( i.e time taken for 2nd unit.)

So time taken for 4th unit will be = 56× 70% = 39.2 hours.

Further time taken for 8th unit will be 70% of 39.2 hours ( i.e. time taken for 4th unit.)

So time taken for 8th unit will be = 39.2 × 70% = 27.44 hours.

Answer: Time taken to complete 8th unit = 27.44 hours.