$4\mathrm{.}1$ A manufacturing company is evaluating replacing a manual material transfer operation with an industrial robot. The current manual operation involves a human worker transferring parts from a conveyor to a pallet, following a specific pattern $($palletizing$).$ Current Manual Operation: $$ Worker picks part from conveyor, moves to pallet, places part: $15$ seconds per part. $$ Worker takes a $15-$minute break mid$-$morning and mid$-$afternoon, plus a $30-$minute lunch break. $$ Assume an $8-$hour shift, with the last $10$ minutes nonproductive for cleanup. $$ The worker can only palletize one part at a time. Proposed Robotic Operation: $$ A robot will perform the palletizing task. $$ The robot's cycle time to pick a part and place it on the pallet varies depending on the location on the pallet. The average robot cycle time is $10$ seconds per part. $$ The robot system has an uptime efficiency of $95\%$ due to random malfunctions. Downtime results in zero production. $$ Programming the robot and setting up the pallet fixture for a new product style takes $90$ minutes. Production runs are typically $400$ parts. $4\mathrm{.}1\mathrm{.}1$ Calculate the average production time per part for the manual operation over an $8-$hour shift, accounting for breaks and cleanup. Assume constant work speed when not on break. $(1)4\mathrm{.}1\mathrm{.}2$ Calculate the production rate in parts per hour for the manual operation over an $8-$hour shift. $(1)4\mathrm{.}1\mathrm{.}3$ Calculate the average production time per part for the robotic operation, accounting for setup time and the production quantity. $(1)4\mathrm{.}1\mathrm{.}4$ Calculate the production rate in parts per hour for the robotic operation, accounting for the uptime efficiency and setup time over the production run. $(1)4\mathrm{.}1\mathrm{.}5$ Based only on the operational characteristics provided $($cycle time, downtimes, etc.$),$ and without considering direct costs yet, analyze the potential benefits and drawbacks of switching to the robotic system for these medium$-$sized batches. Reference specific concepts like cycle time reduction, nonproductive time $($setup vs$.$ downtime$),$ repeatability $($implied benefit for consistent pallet pattern$),$ and the characteristic of a repetitive work cycle. $(3)4\mathrm{.}1\mathrm{.}6$ Briefly mention how the cost of the robot system would need to be factored into a full economic justification, referencing the concept of higher investment cost as a potential disadvantage compared to manual operations. $(3)$