Problem $18-9$

Problem $18-11($Static$)$

One operator services a bank of five machines. Machine running time and service time are both exponential. Machines run for an

average of $90$ minutes between service requirements, and service time averages $35$ minutes. The operator receives $$20$ per hour in

salary and fringe benefits, and machine downtime costs $$70$ per hour per machine. Use Table $1,$ Table $2$ and Table $3.$

a$.$ If each machine produces $60$ pieces per hour while running, find the average hourly output of each machine, when waiting and

service times are taken into account.

Note: Round your answer to $2$ decimal places.

Average hourly output Problem $18-5($Static$)$

A small town with one hospital has two ambulances to supply ambulance service. Requests for ambulances during nonholiday weekends average $0\mathrm{.}45$ per hour and tend to be Poisson$-$distributed. Travel and assistance time averages two hours per call and follows an exponential distribution. Use Table $18\mathrm{.}4.$

a$.$ Find system utilization.

Note: Round your answer to the nearest whole percent.

System utilization

b$.$ Find the average number of customers waiting.

Note: Round your answer to $\backslash (\backslash$mathbf$\{3\}\backslash )$ decimal places.

Average number of customers

c$.$ Find the average time customers wait for an ambulance.

Note: Round your answer to $\backslash (\backslash$mathbf$\{3\}\backslash )$ decimal places.

Average time

hour

d$.$ Find the probability that both ambulances will be busy when a call comes in$.$

Note: Round intermediate calculations to $\backslash (\backslash$mathbf$\{3\}\backslash )$ decimal places and final answer to $\backslash (\backslash$mathbf$\{2\}\backslash )$ decimal places.

Probability