Consider a production flow line with $3$ steps or workstations in series $(1,2,3)$ and ample buffer storage between steps$/$ stations. Every unit must flow through all three stations before it is completed. The average unit processing times at the three stations are $3\mathrm{.}6$ hours, $2\mathrm{.}4$ hours, and $4\mathrm{.}8$ hours, respectively. The line operates continuously; there are $24$ working hours in a day, and $5$ working days per week. There is a single machine at each station and current demand is $4$ units per day. Demand is expected to vary and then stabilize at a peak demand of $14$ units per day.

Instead of knowing the unit process time data at a station, you were given the following: average station utilization over $30$ days $=0\mathrm{.}6$; number of units processed by the station during these $30$ days $=128.$ Estimate the average unit processing time at the station. Show work.