Purple Airlines has ordered 30 small jets from its supplier.The supplier has estimated the first aircraft will require 350 days of direct labor to manufacture and assemble.Based on past experience,the supplier estimates the learning curve to be 75%.Estimate the number of days of direct labor for all 30 jet aircrafts.
A)3,000.5 days
B)4,006.1 days
C)3,456.7 days
D)4,567.3 days

Question

Quizplus · Accepted Answer

The learning curve formula can be used to estimate the time required to produce multiple units of a product when the learning rate is known. The formula is $T_n = T_1 \times n^{\log(b) / \log(2)}$, where $T_n$ is the time to produce the nth unit, $T_1$ is the time to produce the first unit, $n$ is the unit number, and $b$ is the learning rate (in this case, 75% or 0.75). However, to find the total time for all units, we use the cumulative average time per unit formula, which simplifies to $T_{total} = T_1 \times n \times x^{\log(b) / \log(2)}$, where $x = n / 2$ for a learning curve. For 30 jets and a 75% learning curve, the calculation is more complex and involves summing the time for each jet, adjusted for the learning curve. The correct total days of direct labor for all 30 jets, based on the 75% learning curve, aligns with the calculation method for learning curves, resulting in approximately 4,006.1 days.

Purple Airlines Has Ordered 30 Small Jets from Its Supplier