I.$$ Process Analysis and Waiting Lines $($Max $45$ Points$)$: This question is a simplification of the station capacity problem in Littlefield Labs. Consider a production flow line with $3$ steps or workstations in series $(123)$ 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.

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$1.(10$ points$)$ Bottleneck, Process Capacity, Time to Produce $10$ Units: Identify the bottleneck station and calculate the process capacity in parts per day for the current line, with demand of $4$ units $/$ day. Assume no variability, sufficient inventory storage buffers, and steady state operation at the process flow rate: How long do you expect the current line operating normally to take to produce $10$ units?