Problem $2(30$ points$)$: Consider the design of a two$-$workstation flowline

where each workstation is operated as a $\frac{G}{G}\frac{?}{s}$ 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.