Jack Simpson contract negotiator for Nebula Airframe Company

Jack Simpson, contract negotiator for Nebula Airframe Company, is currently involved in bidding on a follow-up government contract. In gathering cost data from the first three units, which Nebula produced under a research and development contract, he found that the first unit took 2,500 labor hours, the second took 2,125 labor hours, and the third took 2,000 hours.

In a contract for three more units, how many labor hours should Simpson plan for? (Round your answer to the nearest whole number.)

Solution

It is given that, T1 = 2500 hours

T2 = 2125 hours

T3 = 2000 hours

Learning rate for second unit, r1 = (T2/T1)^{1/(ln(2)/ln(2))} = (2125/2500)¹ = 0.85

Learning rate for third unit, r2 = (T3/T1)^{1/(ln(3)/ln(2))} = (2000/2500)^0.63 = 0.8687

Average learning rate = (r1+r2)/2 = (0.85+0.8687)/2 = 0.8593

T4 = T1*r^{(ln(4)/ln(2))} = 2500*0.8593² = 1846 hours

T5 = T1*r^{(ln(5)/ln(2))} = 2500*0.8593^2.322 = 1758 hours

T6 = T1*r^{(ln(6)/ln(2))} = 2500*0.8593^2.585 = 1689 hours

Total labor hours required for three more units = 1846+1758+1689 = 5293 hours