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%**

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