Question

4.4 If unit 1 requires 6 labor hours and unit 5 requires 1.8324, what is the learning rate? What will unit 6 require? What have the first five units required in total?

4.6 If unit 1 required 200 hours to produce and the labor records for an Air Force contract of 50 units indicate an average labor content of 63.1 hours per unit, what was the learning rate? What total additional number of labor hours would be required for another Air Force contract of 50 units? What would be the average labor content of this second contract? Of both contracts combined? If labor costs the vendor $10 per hour on this Air Force contract and the price to the Air Force is fixed at $550 each, what can you say about the profitability of the first and second contracts and hence the bidding process in general?

Answer 1

4.4)

Time required for Unit n = Time for 1st unit*n^b

n = Unit number

b = ln(Learning rate)/ln(2)

Time for 5th unit = 1.8324

1.8324 = 6*(5)^b

0.3054 = 5^b

Taking log on both sides:

ln(0.3054) = b*ln(5)

b = -0.7370

ln(Learning rate)/ln(2) = -0.7370

ln(Learning rate) = -0.7370*ln(2) = -0.5108

Learning rate = e^-0.5108 = 0.6

So, Learning rate is 60%

Time required for 6th unit = 6*(6)^b = 6*(6)^-0.7370 = 1.6021 hours

Time for 1st 5 units = 6*Total time factor for 5 units = 6*2.710 = 16.26 hours