The first unit of a product took 80 work days. The learning curve is estimated to be 90%. The time for the fifth unit will be about ________ work days and the time for the first five units will be about ________ work days.
A) 63; 347
B) 250; 51
C) 65; 285
D) 51; cannot be determined
E) 65; cannot be determined

Question

Quizplus · Accepted Answer

To calculate the time for the fifth unit, we need to use the learning curve formula:

Time for n units = A * n^B

where A and B are constants that depend on the degree of learning, and n is the number of units.

With a 90% learning curve, A = 80 and B = -log(0.9) / log(2) = 0.152.

So, for the fifth unit:

Time for 5th unit = 80 * 5^0.152 = 62.69 work days, which rounds up to 63 work days (Choice A).

To calculate the time for the first five units, we need to add up the time for each unit. Using the same formula, we get:

Time for 1st unit = 80 * 1^0.152 = 80 work days
Time for 2nd unit = 80 * 2^0.152 = 65.61 work days
Time for 3rd unit = 80 * 3^0.152 = 57.46 work days
Time for 4th unit = 80 * 4^0.152 = 52.06 work days
Time for 5th unit = 80 * 5^0.152 = 62.69 work days

Total time for 1st five units = 80 + 65.61 + 57.46 + 52.06 + 62.69 = 318.82 work days, which rounds up to 347 work days (Choice A).

The First Unit of a Product Took 80 Work Days