Weston,Inc.,produces widgets.To manufacture a new type of widget,it took 12 iterations before the process reached a steady state of 42 hours.If Weston has a 79% learning rate,use the logarithmic approach to calculate the time it took to manufacture the first widget.
A)95.89 hours
B)98.50 hours
C)97.78 hours
D)95.66 hours

Question

Quizplus · Accepted Answer

According to the logarithmic approach, the formula for calculating the time it took to manufacture the nth widget is:

Tn = T1 * n^log(r)/log(2)

where Tn is the time taken to manufacture the nth widget, T1 is the time taken to manufacture the first widget, n is the number of widgets produced, and r is the learning rate.

Using the given information, we can calculate the time taken to manufacture the 12th widget as:

42 = T1 * 12^log(0.79)/log(2)

42/T1 = 12^log(0.79)/log(2)

Taking the logarithm of both sides, we get:

log(42/T1) = log(12^log(0.79)/log(2))

log(42/T1) = log(12) * log(0.79)/log(2)

log(42/T1) = 1.079 * (-0.3219)

log(42/T1) = -0.3472

T1 = 42/10^(-0.3472)

T1 = 97.78 hours

Therefore, the best choice is C) 97.78 hours.