Question

uct B, 50 units per day; and product C, 60 units per day. What is the bottleneck? What is the flow rate for each flow unit assuming that demand must be served in the mix described above (i.e., for every four units of A, there are five units of B and six units of C)? (Cranberries) International Cranberry Uncooperative (ICU) is a competitor to the Na- tional 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 trucks are sfficiently small so that the delivery of cranberries can be treated as a continu- ous inflow. The first truck arrives at 6:00 A.M. and unloads immediately, so processing be- gins 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. 03.3 What is the maximum number of barrels of cranberries that are waiting on the trucks at a. any given time? b. At what time do the trucks stop waiting? c. At what time do the bins become empty? d. ICU is considering using seasonal workers in addition to their regular workforce to help with the processing of cranberries. When the seasonal workers are working, the pro- cessing rate increases to 125 barrels per hour. The seasonal workers would start work- ing at 10:00 A.M. and finish working when the trucks stop waiting. At what time would ICU finish processing the cranberries using these seasonal workers? (Western Pennsylvania Milk Company) The Western Pennsylvania Milk Company is producing milk at a fixed rate of 5,000 gallons/hour. The company's clients request 100,000 Q3.4

Answer 1

Answer 1:- Cranberries arrive at a rate of 150 barrels per hour. They get processed at a rate of 100 barrels per hour. Thus, inventory accumulates at a rate of 150-100=50 barrels per hour. This happens while trucks arrive, i.e. from 6 am to 2 pm. The highest inventory level thereby is 8h*50 barrels per hour=400 barrels. From these 400 barrels, 200 barrels are in the bins, the other 200 barrels are in trucks.

Answer 2:- From 2 pm onwards, no additional cranberries are received. Inventory gets depleted at a rate of 100 barrels per hour. Thus, it will take 2 hours until the inventory level has dropped to 200 barrels, at which time all waiting cranberries can be stored in the bins. Thus, trucks stop waiting at 4 p.m

Answer 3:- It will take another 2 hours until all the bins are empty because inventory depletes at 100 barrels per hour and the bins hold 200 barrels. Therefore, bins become empty at 6 p.m

Answer 4:- Since the seasonal workers only start at 10:00 am, the first 4 hours of the day we accumulate 4 hours * 50 barrels per hour=200 barrels. For the remaining time that we receive incoming cranberries, our processing rate is higher (125 barrels per hour). Thus, inventory only accumulates at a rate of 25 (150-125 barrels per hour). Given that this happens over 4 hours, we get another 100 barrels of inventory. At 2 pm, we thereby have 300 barrels in inventory. After 2 pm, we receive no further cranberries but 100 barrels worth of inventory is waiting in trucks. Since seasonal workers operate till no trucks, trucks stop waiting after 100 barrels are processed at a rate of 125 barrels per hour, which takes 100 barrels / 125 barrels/hour=0.8 hours=48 minutes. From then, we need another 2 hours at the regular processing rate of 100 barrels per hour to empty the 200 barrels in the bins. Thus, we finish at 4:48 p.m.