Problem $1$ Floor$-$On Ltd$.,$ operates a line that produces self$-$adhesive tiles. This line consists of single$-$machine stations and is almost balanced $($i$.$e$.,$ station rates are nearly equal$).$ A manufacturing engineer has estimated the bottleneck rate of the line to be $2,000$ cases per $16-$hour day and the raw. process time to be $30$ minutes. The line has averaged $1,700$ cases per day, and cycle time has averaged $3\mathrm{.}5$ hours.

$($a$)$ What would you estimate average WIP level to be$?$

$($b$)$ How does this performance compare to the practical worst case?

$($c$)$ What would happen to the performance of the line if we increased capacity at a nonbottleneck station and held WIP constant at its current level?

$($d$)$ What would happen to the performance of the line if we replaced a single$-$machine station with four machines whose capacity equaled that of the single machine and held the WIP constant at its current level?

$($e$)$ What would happen to the performance of the line if we began moving cases of tiles between stations in large batches instead of one at a time?