Answer:
Approximately 18 units will be produced before the output rate exceeds 12 units per hour.
Step-by-step explanation:
The learning curve formula is given by:
[tex]Y = aX^{b}[/tex]
In which:
Y is the average time per unit.
X is the cumulative number of units produced.
a is the time required to produe the first unit
b = log of learning rate/log 2
In our problem, we have:
Y = 12 units per hour. We are working in minutes, what is the average time per unit?
60 minutes - 12 units
Y minutes - 1 unit
[tex]12Y = 60[/tex]
[tex]Y = 5[/tex]
So Y = 5.
X is the value we want to find
a = 30
b = [tex]\frac{log 0.65}{log 2}=-0.6215[/tex]
So
[tex]Y = aX^{b}[/tex]
[tex]5 = 30X^{-0.6215}[/tex]
[tex]\frac{1}{6} = \frac{1}{X^{0.6215}}[/tex]
[tex]X^{0.6215} = 6[/tex]
[tex]\sqrt[0.6215]{X^{0.6215}} = \sqrt[0.6215]{6}[/tex]
[tex]X = 17.86[/tex]
Approximately 18 units will be produced before the output rate exceeds 12 units per hour.
