In addition, ${}_1-100,{}_2=150,{}_{AB}=0\mathrm{.}4,{}_{BC}=0\mathrm{.}3,$ and ${}_{DE}=0\mathrm{.}7.$ Assume the arrival rates are exponential and all service times are also exponentially distributed. Also, assume the arrival rates and service rates are expressed in units of jobs$/$hours$.$

Solve the problem for the following performance measures either manually or with Excel:

a$)$ The utilization of each station in the system

b$)$ The average number of jobs in the system at any point in time $($L$)$

c$)$ The average time spent in the system by a Job $($W$)$

d$)$ Validate your solution in $($b$)$ and $($c$)$ using either the Python Program we used in class or by using Simio Simulation.