The first unit of production took 10 hours with an 80% learning curve. How long will it take to complete both the first and second units?
A) 10 hours
B) 8 hours
C) 18 hours
D) none of the above
E) There is not enough information to solve the problem.

Question

Quizplus · Accepted Answer

The learning curve formula is:
Y = aX^b
where Y is the time to produce a unit, X is the number of units produced, a is the time to produce the first unit, and b is the learning rate (percentage improvement from the previous unit to the current unit).

For this problem, we are given that the first unit took 10 hours and has an 80% learning curve:
Y(1) = 10
b = log(0.8) / log(2) = -0.3219

To find the time to produce the second unit, we use the learning curve formula for X = 2:
Y(2) = a(2)^b = 10(2)^(-0.3219) = 7.68

Therefore, the total time to produce both the first and second units is:
10 + 7.68 = 17.68 hours, which rounds up to 18 hours. Thus, the answer is C.

The First Unit of Production Took 10 Hours with an 80