Respuesta :
Answer:
(a) 6.5774 minutes
(b) 4.3879 minutes
(c) 2.459 minutes
(d) 245.902 minutes
Explanation:
The learning curve model follows the following equation:
[tex]Y=aX^b[/tex]
where Y are the units time to produce X units, and a is the time for assembly the first unit. Additionally, b is calculated as:
[tex]b=\frac{ln(r)}{ln(2)}[/tex]
Where r is the learning rate for mechanical assembly. So, b is equal to:
[tex]b=\frac{ln(0.84)}{ln(2)}=-0.2515[/tex]
Then, the equation is:
[tex]Y=7.83X^{-0.2515}[/tex]
Finally, the unit times to produce the second unit are:
[tex]Y=7.83(2)^{-0.2515}=6.5774[/tex]
The 10th unit:
[tex]Y=7.83(10)^{-0.2515}=4.3879[/tex]
The 100th unit:
[tex]Y=7.83(100)^{-0.2515}=2.459[/tex]
Then, the total cumulative time T to produce 100 units in the Crawford model is calculated as:
[tex]T=7.83\frac{(100.5)^{1-0.2515}-(0.5)^{1-0.2515})}{1-0.2515} \\T=323.5383[/tex]
