A production line at $xYZ$ Inc. has five stations.

Station one can process a unit in $15$ minutes. The unit then flows to Station two, which can process a unit in $18$ minutes.

The third station can process a unit in $12$ minutes. $($This station operates separately from. and simultaneously with stations one and two, which are independent and sequential operations$).$

Next, the unit from Station $2$ and Station $3$ flow to Station $4.$ Station $4$ can process a unit in $17$ minutes.

The fifth station has three identical machines, each of which can process a unit in $30$ minutes $($each unit only needs to be processed on one of the three machines$).$

a$.$ The bottleneck of the process is with an hourly capacity of

b$.$ If XYZ Inc. added a second identical machine at Station $2,$ what is the new bottleneck and capacity of the system

c$.$ What is the throughput time for XYZ Inc. to make $1$ unit?