Q$3(4$ points$)$ 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. $(3$ points$)$

$($b$)$ At what time will the last truck depart the barn? $(1$ point$)$