The Western Pennsylvania Milk Company is producing milk at a fixed rate of 5,000 gallons/hour. The company's clients request 100,000 gallons of milk over the course of one day. This demand is spread out uniformly from 8 a.m. to 6 p.m. If there is no milk available, clients will wait until enough is produced to satisfy their requests.
The company starts producing at 8 a.m. with 25,000 gallons in finished goods inventory. At the end of the day, after all demand has been fulfilled, the plant keeps on producing until the finished goods inventory has been restored to 25,000 gallons. When answering the following questions, treat trucks/milk as a continuous flow process. Begin by drawing a graph indicating how much milk is in inventory and how much milk is "back-ordered" over the course of the day.
a. At what time during the day will the clients have to start waiting for their requests to be filled?
b. At what time will clients stop waiting?
c. Assume that the milk is picked up in trucks that hold 1,250 gallons each. What is the maximum number of trucks that are waiting?
d. Assume the plant is charged $50 per hour per waiting truck. What are the total waiting time charges on a day?