A large fully automated municipal incinerator is being designed. A survey estimates the garbage load to be 1440 tons/day. This will be harvested by a fleet of compaction trucks which will disgorge their loads into an underground storage bin. A conveyor will then feed the garbage to the incinerator.

The proposed daily collection route is such that at the beginning of the working day (6 A.M. sharp!) relatively large quantities of garbage (average of 6 tonslmin) are returned from nearby commercial areas. 

Subsequently, the supply will diminish as more remote suburban areas are serviced. It is assumed that the collection rate is proportional to the amount of garbage still to be collected, the initial rate being one truckloadlmin. The conveyor, on the other hand, will transport garbage at a uniform 1 tonlmin to the incinerator. At the beginning of the working day, the trucks will work faster than the conveyor; later in the day, slower. Thus, each day the bin will accumulate material, then lose material.

To evaluate this operation, we need information. Please help us with this.

(a) At what time of day will the trucks have collected 95% of the day's garbage?

(b) How much garbage whould the storage bin be designed for?

(c) At what time of day will the bin be fullest?

(d) At what time of day will the bin be empty?