it cost a contactor $13750 to manufacture their first unit. The company expects to experience a 93% unit learning curve. Estimate the cost of the 14th unit. (Round intermediate calculation to 4 decimal places)?
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To estimate the cost of the 14th unit using the unit learning curve, we need to use the learning curve formula:
Cost of n-th unit = Cost of 1st unit * (n^x)
Where:
- n is the unit number
- x is the learning curve index, expressed as a decimal
In this case, the learning curve index is 0.93, which is equivalent to a 93% learning curve.
Let's calculate the cost of the 14th unit:
n = 14
x = log(0.93) / log(2) = -0.0817 (rounded to 4 decimal places)
Cost of 14th unit = $13,750 * (14^(-0.0817))
Calculating:
Cost of 14th unit = $13,750 * (14^(-0.0817))
≈ $13,750 * 0.8893
≈ $12,218.725
Therefore, the estimated cost of the 14th unit is approximately $12,218.725.
To estimate the cost of the 14th unit using the unit learning curve, we need to know the learning curve percentage and the cost of the first unit.
The unit learning curve formula is as follows:
Cost of nth unit = Cost of first unit * (n^log(LC)),
where:
- Cost of nth unit is the cost of the unit we want to estimate (14th unit in this case)
- Cost of first unit is the cost of the initial unit ($13,750 in this case)
- n is the cumulative production quantity (14 in this case)
- LC is the learning curve percentage (93% in this case)
Now, let's substitute the values into the formula:
Cost of 14th unit = $13,750 * (14^log(93%))
To calculate this equation, we need to convert the learning curve percentage into decimal form because the log function requires the input to be in that form. So, 93% becomes 0.93.
Cost of 14th unit = $13,750 * (14^log(0.93))
Using a calculator, we can calculate the cost of the 14th unit.
Cost of 14th unit ≈ $13,750 * (14^log(0.93)) ≈ $13,750 * (14^0.0349) ≈ $13,750 * 1.0878 ≈ $14,977.76
Therefore, the estimated cost of the 14th unit is approximately $14,977.76 (rounded to 4 decimal places).