Question

LEARNING CURVE There are 2 firms: Company A and Company B. 1. Company A took 150...

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

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

Now, using the equation,

Y = aXb

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 = aXb

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 = aXb

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%