A process with five steps has a cycle time of $1\mathrm{.}8$ minutes per unit. The only inventory in the system is held before the last station, where $50$ units of inventory are maintained. A defective unit is produced at the first station but is not detected until final inspection $($after the fifth station$).$

What is the information turnaround time $($in minutes$)?$

$($Example: A process with five steps has a cycle time of $2\mathrm{.}6$ minutes per unit. The only inventory in the system is held before the last station, where $23$ units of inventory are maintained. A defective unit is produced at the third station but is not detected until final inspection $($after the fifth station$).$

Example explanation: A defective unit produced by the third workstation must journey through the remaining two stations and wait in inventory before being observed in inspection. Therefore, the unit will remain undetected for $2\backslash$times $2\mathrm{.}6+23\backslash$times $2\mathrm{.}6=5\mathrm{.}2+59\mathrm{.}8=65$ minutes. $)$