OceanBlue is a fish cannery $$ a facility where fish is continuously processed and then canned. All fish coming into the cannery must be either processed and canned immediately or stored in a freezer $($to be processed whenever possible$).$ Given the high speed and high volume of the process, the theoretical flow time of the process is negligible. Suppose that daily input of fish to the cannery follows the following pattern: $($i$)100$ tons$/$hr between $8$ a$.$m$.$ and $1$ p$.$m$.($ii$)75$ tons$/$hr between $1$ p$.$m$.$ and $3$ p$.$m$.($iii$)50$ tons$/$hr between $3$ p$.$m$.$ and $5$ p$.$m$.$ The processing capacity of the cannery is: $($i$)100$ tons$/$hr between $8$ a$.$m$.$ and $11$ a$.$m$.($ii$)50$ tons$/$hr between $11$ a$.$m$.$ and $2$ p$.$m$.($iii$)100$ tons$/$hr between $2$ p$.$m$.$ and $5$ p$.$m$.($a$)$ Draw an inventory build$-$up diagram $($the continuous version$)$ that shows the amount of unprocessed fish in the freezer from $8$ a$.$m$.$ to $5$ p$.$m$.($b$)$ What is the average amount of unprocessed fish stored in the freezer through the day $(1$ day $=9$ hours$)$