An 80% learning curve has been observed for the production of the MEERKAT system. If the 5th production unit''s recurring cost is $1 million, what will be the recurring cost for the 10th production unit? Assume that the production line is continuous and that the learning curve does not change.
a. $800,000
b. $900,000
c. $640,000
d. $500,000
a is the correct answer.
To calculate the recurring cost for the 10th production unit using an 80% learning curve, we can use the following formula:
Cost = Cost of 1st Unit * (Number of Units^x)
Where:
- Cost of 1st Unit: $1 million
- Number of Units: 10
- x: Log of the learning curve as a decimal (80% = 0.8)
Let's calculate the recurring cost:
Cost = $1 million * (10^0.8)
Using a scientific calculator or a calculator with a logarithm function, you can find that 10^0.8 is approximately 5.01187.
Cost ≈ $1 million * 5.01187
Cost ≈ $5,011,870
So, the recurring cost for the 10th production unit would be approximately $5,011,870.
Therefore, the correct answer is not listed among the provided options.
To calculate the recurring cost for the 10th production unit using an 80% learning curve, we can use the following formula:
Recurring cost for a given production unit = Recurring cost for the first production unit * Number of units^log(learning curve percentage)
In this case, the recurring cost for the 5th production unit is given as $1 million and the learning curve percentage is 80%.
Let's substitute these values into the formula:
Recurring cost for the 5th production unit = $1 million
Number of units = 5
Learning curve percentage = 80%
Recurring cost for the 5th production unit = $1 million * (5^log(80%))
Recurring cost for the 5th production unit = $1 million * (5^0.9031)
Recurring cost for the 5th production unit ≈ $1 million * (4.1753)
Recurring cost for the 5th production unit ≈ $4,175,300
Now, to calculate the recurring cost for the 10th production unit, we need to substitute the number of units as 10 into the formula:
Recurring cost for the 10th production unit = Recurring cost for the 5th production unit * (10^log(80%))
Recurring cost for the 10th production unit = $4,175,300 * (10^0.9031)
Recurring cost for the 10th production unit ≈ $4,175,300 * (8.9957)
Recurring cost for the 10th production unit ≈ $37,555,463.91
Therefore, the recurring cost for the 10th production unit, rounded to the nearest dollar, is approximately $37,555,464.
So, the correct answer is not among the provided options.