Part $4$: WIP in the System $($Continued$)$

Management is concerned about the quality of units that emerge from Task $1.$ They have observed that the cutting tool wears down throughout the day, which reduces the precision of parts processed at Task $1.$ To remedy this, management proposes that after every $240$ units, the cutting tool on the machine will be replaced. Replacement will take $30$ minutes, during which time Task $1$ will be unable to process any units. After replacement, Task $1$ then immediately begins to process units, and the processing times of both tasks are otherwise unaffected by this change. Assume that at $8$ am$,$ the cutting tool in work station $1$ has just been replaced $($i$.$e$.,$ it doesn$$t need to be replaced until $240$ units are cut$)$ and the turning machine in station $2$ has been off all night.