Q$3\mathrm{.}3($Static$)$ Cranberry $[3\mathrm{.}3]$

International Cranberry Uncooperative $($ICU$)$ is a competitor to the National Cranberry Cooperative $($NCC$).$ At ICU, barrels of cranberries

arrive on trucks at a rate of $150$ barrels per hour and are processed continuously at a rate of $100$ barrels per hour. Trucks arrive at a

uniform rate over eight hours, from $6$:$00$ a$.$m$.$ until $2$:$00$ p$.$m$.$ Assume the delivery of cranberries can be treated as a continuous inflow.

The first truck arrives at $6$:$00$ a$.$m$.$ and unloads immediately, so processing begins at $6$:$00$ a$.$m$.$ The bins at ICU can hold up to $200$

barrels of cranberries before overflowing. If a truck arrives and the bins are full, the truck must wait until there is room in the bins.

a$.$ What is the maximum number of barrels of cranberries that are waiting on the trucks at any given time?

Maximum number of barrels

b$.$ How many additional hours beyond $2$:$00$ pm must the last truck wait until its inventory is depleted?

Note: Round the answer to $2$ decimal places.

It will take

hours after $2pm,$ after which no more trucks will be waiting.

c$.$ How many additional hours beyond $2$:$00$ pm will be required until the bins become empty?

Note: Round the answer to $2$ decimal places.

It will take

hours until all the bins are empty.