Braum’s has a fine herd of cows that are content to produce milk at the rate of 500t+1000 gallons/hour (where t=hour of the day) from 4 am to 2 pm. Amish farmers milk their cows like crazy and load the milk onto tanker trucks bound for their pasteurization and bottling plant. The bottling plant can process milk at the rate of 5000 gallons per hour and they have a big tub they use to hold any milk that arrives that exceeds their processing capacity in a given hour. The tub holds 5000 gallons, and when it is full, any arriving trucks have to wait to dump their load. Now even though the trucks are large, when answering questions 3-5, treat trucks/milk as a continuous flow process – imagine a steady stream of tiny trucks making their way from farms to the plant.

1.At what time during the day will the trucks have to start waiting for some space to free up in the big tub?

2.At what time is inventory at its zenith?

3.At what time will trucks stop waiting?

4.Now assume that the milk is picked up in trucks that hold 1,000 gallons each. What is the maximum number of trucks that are waiting?

5.How much milk is processed by the end of the day?