Berringer Designs hired a graphic artist.It is estimated that the artist's learning rate is at 70% and her ﬁrst quarter's output amounted to 300 relatively equal job outputs, which took her a total of 50 hours to complete.Output is expected to double in every succeeding quarter. By the 5th quarter, based on learning curve estimates, what should the artist's average time (in hours) be for the units of output?
A)17.15 hours.
B)3.5 hours.
C)12.005 hours.
D)6.9 hours.
E)None of the answers is correct.

Question

Quizplus · Accepted Answer

We can use the following formula for learning curve:

Y = aX^b

Where:
Y = time per unit 
X = cumulative production in units 
a = time taken for the first unit
b = the learning rate (expressed as a decimal)

From the given data, we can find the values of "a" and "b":

a = 50 hours (total time taken for the first quarter)
b = log(0.7)/log2 = -0.151 (since the learning rate is given as 70%)

For the 5th quarter, the cumulative production would be:

X = 2^4 + 2^3 + 2^2 + 2^1 + 2^0 = 31 units of output

Using this value of X and the values of "a" and "b" in the formula, we get:

Y = 50(31^-0.151) = 12.005 hours

Therefore, the artist's average time per unit of output in the 5th quarter should be 12.005 hours (option C).

Berringer Designs Hired a Graphic Artist