Respuesta :
Answer:
a) 86%
b) 2nd unit = 82 hs.
3rd unit = 75 hs
c) 100th unit = 36 hs
Step-by-step explanation:
We can model the learning curve for manufacturing the units as:
[tex]t=aX^b[/tex]
where t is the time for the Xth unit, and a and b are parameters that we will calculate from the data,
We know that t(1)=95. Then, we have:
[tex]t(1)=a\cdot 1^b=95\\\\a=95[/tex]
And we know that the fourth unit (X=4) take 71 hours to be completed (t(4)=71). Then, we can calculate the other parameter as:
[tex]t(4)=95\cdot4^b=71\\\\4^b=71/95\approx 0.7473\\\\b\cdot ln(4)=ln(0.7473)\\\\b=ln(0.7473)/ln(4)=-0.291/1.386\\\\b=-0.21[/tex]
We have the model for the learning curve:
[tex]t=95X^{-0.21}[/tex]
The learning rate percentage is calculated from the b parameter:
[tex]b=\dfrac{ln(LRP)}{ln(2)}=-0.21\\\\\\ln(LRP)=-0.21*ln(2)=-0.21*0.693=-0.1455\\\\LRP=e^{-0.1455}=0.86[/tex]
The learning rate percentage is 86%.
b) The most likely times required for the 2nd and 3rd units are calculated with the model:
[tex]t(2)=95\cdot2^{-0.21}=95*0.864=82\\\\t(3)=95\cdot3^{-0.21}=95*0.794=75[/tex]
c) If we use the model to calculate the time required for the 100th unit, we have:
[tex]t(100)=95\cdot100^{-0.21}=95*0.38=36[/tex]
