Respuesta :
Answer:
a) Mean arrival rate in jobs per hour = 0.6250
b) Mean service rate in jobs per hour = 0.7692
c) The average number of jobs waiting for service = 2.802
d) Average time a job waits before the welder can begin working on it = 4.5 hours
e) Average number of hours between when a job is received and when it is completed = 5.8 hours
f) Percentage of the time is Gubser's welder busy = 81%
Explanation:
As given,
Number of jobs = 5
Rate = 8 hour per day
Average hours = 1.3
Standard deviation - 1 hour
a)
Mean arrival = [tex]\frac{No. of jobs}{rate}[/tex]
= [tex]\frac{5}{8}[/tex] = 0.6250 per hour
⇒Mean arrival rate in jobs per hour = 0.6250
b)
Mean service rate = [tex]\frac{hour}{average hour}[/tex]
= [tex]\frac{1}{1.3}[/tex] = 0.7692 per hour
⇒Mean service rate in jobs per hour = 0.7692
c)
Average number of job waiting for service = [tex]\frac{(0.6250)^{2} (1)^{2} + \frac{0.6250}{0.7692} }{2 ( 1 - \frac{0.6250}{0.7692} )}[/tex]
= [tex]\frac{1.05}{0.375}[/tex] = 2.802
⇒The average number of jobs waiting for service = 2.802
d)
Average time a job waits before the welder can begin working on it = [tex]\frac{2.802}{0.6250}[/tex]
= 4.5 hr
⇒Average time a job waits before the welder can begin working on it = 4.5 hours
e)
Average number of hours between when a job is received and when it is completed = 4.5 + [tex]\frac{1}{0.7692}[/tex]
= 4.5 + 1.3
= 5.8 hours
⇒Average number of hours between when a job is received and when it is completed = 5.8 hours
f)
Percentage of the time is Gubser's welder busy = [tex]\frac{0.6250}{0.7692}[/tex] ×100%
= 0.8125×100%
= 81.25% ≈ 81%
⇒Percentage of the time is Gubser's welder busy = 81%
