a manager is trying to estimate the appropriate learning curve for a certain job. the manager notes that the first four units had a total time of 30 min. which learning curve would yield approximately this result if the firs unit took 10 minutes. A) .70 B).75 C) .80 D) .85 E) .90
To determine the appropriate learning curve for the job, we need to understand the concept of a learning curve. A learning curve is a mathematical representation that shows the relationship between the time taken to complete a task and the cumulative number of units produced or completed. It assumes that as more units are produced, the time required to complete each unit decreases.
In this particular case, we are given that the first unit took 10 minutes, and the first four units in total took 30 minutes. We need to find the learning curve that would yield approximately this result.
To find the appropriate learning curve, we can use the learning curve formula:
Tⁿ = a * N^b
Where:
Tⁿ = time taken for the nth unit
N = cumulative number of units produced
a = time taken for the first unit
b = log (learning curve ratio) / log (2)
We can rearrange the formula to solve for the learning curve ratio:
learning curve ratio = (Tⁿ / a)^(1 / b)
Let's calculate the learning curve ratios for the given options:
Option A) learning curve ratio ≈ (30 / 10)^(1 / b)
Option B) learning curve ratio ≈ (30 / 10)^(1 / b)
Option C) learning curve ratio ≈ (30 / 10)^(1 / b)
Option D) learning curve ratio ≈ (30 / 10)^(1 / b)
Option E) learning curve ratio ≈ (30 / 10)^(1 / b)
Now, we need to compare these learning curve ratios to the four units' time of 30 minutes. Whichever learning curve ratio yields a value close to 30 minutes is the appropriate one.
Calculating the learning curve ratios for each option, we have:
Option A) learning curve ratio ≈ (30 / 10)^(1 / b) ≈ 1.73^(1 / b)
Option B) learning curve ratio ≈ (30 / 10)^(1 / b) ≈ 1.73^(1 / b)
Option C) learning curve ratio ≈ (30 / 10)^(1 / b) ≈ 1.73^(1 / b)
Option D) learning curve ratio ≈ (30 / 10)^(1 / b) ≈ 1.73^(1 / b)
Option E) learning curve ratio ≈ (30 / 10)^(1 / b) ≈ 1.73^(1 / b)
To find the learning curve that yields approximately 30 minutes, we need to try different values for b. We start with b = 0.1 and increase it by small increments until we find a close value.
Checking the calculations for each option:
Option A) learning curve ratio ≈ 1.73^(1 / 0.1) ≈ 1.73^10 ≈ 27.59
Option B) learning curve ratio ≈ 1.73^(1 / 0.1) ≈ 1.73^10 ≈ 27.59
Option C) learning curve ratio ≈ 1.73^(1 / 0.1) ≈ 1.73^10 ≈ 27.59
Option D) learning curve ratio ≈ 1.73^(1 / 0.1) ≈ 1.73^10 ≈ 27.59
Option E) learning curve ratio ≈ 1.73^(1 / 0.1) ≈ 1.73^10 ≈ 27.59
None of the calculated learning curve ratios are close to the observed time of 30 minutes for the first four units. Therefore, none of the options A, B, C, D, or E yield this result.
This means that we cannot determine the appropriate learning curve based on the provided information.