$1.$ Specify the possible system states.

$2.$ Find the relative workload factor for each machine. Which machine has the heaviest load?

$3.$ Give and expression for the utilization of machine $1$ in terms of the system states defined in part a$.$ A three$-$machine workcell is controlled such that six jobs are kepy in process at all times. Four part types are produced. When a job is completed, a new job is dispatched to the system. The new job is selected randomly in proportion to the desired relative production rates of the four part types. The table gives demand and processing data. In each operation in the process plan, the data pair contains $($machine$,$ job processing time$).$ Consider an exponential server, single aggregate part, closed queueing network model of the cell.