Question

3) A product has an average labor cost of $10/hr. The overhead expenses are 100% of labor cost. Time for the first unit-10 hours. Time for the fourth unit= 8.1 hours. Answer the following questions: (10 Points) a) Find the learning curve percentage for the production of this product b) What is the labor cost and overhead cost for the 500-th unit?

Answer 1

1)

We know that normal form of learning curve is given by

Y_x=Kxⁿ

Where

K=Direct labor hours needed for first unit=10 hours

x=unit number=4

Y_x= labor hours needed for x^th unit i.e. 4th unit=8.1 hours

n=log₁₀b/log₁₀2 and b=learning percentage

We can estimate the value of n with the help of given equation

Y_x=Kxⁿ

8.1=10*4n

0.81=4n

Taking natural log both sides

ln(0.81)=nln(4)

n=ln(0.81)/ln(4)=-0.152

Now we can find the value of b

n=log₁₀b/log₁₀2

-0.152=log10b/0.301030

log₁₀b=-0.152*0.301030=-0.04576

b=10^-0.04576=0.90

So, Learning percentage=90%

b)

Let us find the time required for 500th unit

Y_x=Kxⁿ

^Y₅₀₀=10*(500)^-0.152=3.888 minute

Labor Cost=3.888*10=$38.88

Overhead =10% of labor cost=38.88*10%=$3.89