Problem $2(30$ points$)$: Consider the design of a two$-$workstation flowline where each workstation is operated as a G$/$G$/$s queue.

The required processing capacity for this line is $5$ jobs per hour, and the expected cycle time of the jobs when the line is operated at its capacity, should be no more than one hour.

Currently, it has been determined that the first workstation of the line will have a single server with normally distributed processing times. The mean and the variance for this distribution will be $10$min and $25mi{n}^2.$ Also, jobs will be loaded in this workstation with a deterministic pace that is consistent with the target capacity of the line.

The second workstation will employ some servers with mean processing time of $20$min.

Determine $($i$)$ the smallest number of servers for the second workstation and $($ii$)$ the corresponding maximal st$.$ deviation of its processing times that will satisfy the posed specifications.