A defence contractor has just started producing engines for a new government contract.The first engine took 800 hours to produce.If the learning curve is 80%,how long will it take to produce the first 20 engines? (Use at least three decimals in the exponent if you use the logarithmic approach,or use Table E.3 cumulative coefficient. )
A)less than or equal to 1000 hours
B)from 1000 to 8000 hours
C)from 8000 to 8500 hours
D)from 8500 to 10000 hours
E)10,000 or more hours

Question

Quizplus · Accepted Answer

We can use the learning curve formula to find the time it takes to produce the first 20 engines:

Time for 2nd unit = First unit time x (learning %)^log(base 2) of (units produced/units for doubling)
Time for 2nd unit = 800 x (0.80)^log(base 2) of (2/1)
Time for 2nd unit = 800 x 0.80 = 640

To find the time for the 20th unit, we need to first find how many doubling periods it takes to get from 1 to 20 units:

log(base 2) of 20/1 = 4.32

Therefore, it takes 4.32 doubling periods to get from 1 to 20 units. Now we can use the learning curve formula again:

Time for 20th unit = First unit time x (learning %)^log(base 2) of (units produced/units for doubling)
Time for 20th unit = 800 x (0.80)^4.32 = 8444.4

So the time it takes to produce the first 20 engines is between 8000 and 8500 hours, which is choice C.

A Defence Contractor Has Just Started Producing Engines for a New