The time needed for the 30th unit in a process with an 80% learning curve, where the 10th procedure took 90 minutes and machine time is 240 minutes, is most nearly:

To determine the time needed for the 30th unit in a process with an 80% learning curve, we start by understanding the implications of a learning curve in manufacturing. The learning curve effect indicates that as more units of a product are produced, the time taken to produce each subsequent unit decreases at a predictable rate.

In this case, the learning curve percentage is 80%, suggesting that with each doubling of production quantity (e.g., from 10 to 20 units), the time required to produce the next sets of units will be 80% of the previous time taken for the same number of units.

The time for the 10th unit has been given as 90 minutes. The formula to calculate the time for a specific unit (T_n) using a learning curve is:

[

T_n = T_1 \times n^{\log_2LR}

]

Where:

• ( T_1 ) is the time for the first unit,

• ( n ) is the unit number,

• ( LR ) is the learning rate (in this case, 0.8),

• ( \log_2LR ) is the log of the learning rate to base 2.

To find the