The time taken to produce the first unit of a product is 111 minutes. A learning curve of 88% can be applied with the production. Determine the time required (in minutes) to produce the 77th unit.
Question
The time taken to produce the first unit of a product is 111 minutes. A learning curve of 88% can be applied with the production. Determine the time required (in minutes) to produce the 77th unit.
Solution
To solve this problem, we will use the formula for the learning curve, which is:
Tn = T1 * n^log(b)
Where:
- Tn is the time required to produce the nth unit
- T1 is the time required to produce the first unit
- n is the unit number
- b is the learning curve index (in this case, 88% or 0.88)
- log is the logarithm base 2
Step 1: Convert the learning curve index to a logarithm. The learning curve index of 88% or 0.88 becomes log(0.88) = -0.0555 (rounded to 4 decimal places).
Step 2: Multiply the unit number by the logarithm of the learning curve index. In this case, 77 * -0.0555 = -4.2735.
Step 3: Use the result from Step 2 to calculate the time required to produce the 77th unit. The formula becomes T77 = 111 * 2^-4.2735.
Step 4: Calculate the result. T77 = 111 * 2^-4.2735 = 7.68 minutes (rounded to 2 decimal places).
So, it will take approximately 7.68 minutes to produce the 77th unit.
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