Question

LEARNING CURVE
There are 2 firms: Company A and Company B.

1. Company A took 150 hours to produce its first unit.
This month it wants to product 500 units.
Using 80% learning curve, how many hours will it take to produce those 500 units?

2. Comany B also produced 500 units.
However, it took B only 50 hours to produce its first unit.
What was was B's learning curve?

Can someone show me step by step please

Answer 1

We will use the Wrights learning curve model to solve this problem

Now, using the equation,

Y = aX^b

where a = time taken to produce first unit

b = = log of the learning rate/log of 2.

X = Cumulative number of units to be produced

Y = Cumulative average time to produce X units

In this question, for 80% learning curve b = log (0.8)/log 2

= -.09691/.301

= -.32196

COMPANY A

Time taken to produce 1st unit (a) = 150 hours

Learning curve rate = 80%

Total units to be produced (X) = 500

Let average time taken to produce those 500 units = Y

Y = aX^b

Y = 150(500)^-0.32196

Y = 20.282 hours

Thus total time to produce 500 units = 500*20.282 = 10141.46 hours

COMPANY B

Time taken to produce 1st unit (a) = 50 hours

Total units to be produced (X) = 500

Let average time taken to produce those 500 units = Y

Learning curve rate = x%

b = log(x/100) / log 2

Y = aX^b

Y would remain the same as company B also produced the units in the same total amount of time.

20.282 = 50(500)^{log(x/100) / log 2}

20.282 / 50 = (500)^{log(x/100) / log 2}

0.4056 = (500)^{log(x/100) / log 2}

Taking log on both sides and solving

-0.0437 = log(x/100)

10^-0.0437 = x / 100

x = 90.427%

Hence learning curve rate for company B is 90.427%