Q$3$ Apple$-$filled trucks arrive at a barn at the rate $20$ every hour from $8$:$00$ am to $6$:$00$ pm$.$ Each truck contains $20$ bushels. The apples are sorted and packed at a rate of $300$ bushels per hour. The storage capacity of the barn is limited to $600$ bushels and once the barn is full, the trucks must wait to unload their contents.

$($a$)$ Draw the inventory build$-$up diagram.

$($b$)$ At what time will the last truck depart from the barn?