Question

At the International Cranberry Uncooperative (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 sufficiently small so that the delivery of cranberries can be treated as a continuous inflow. There are two bins at ICU; each bin can hold up to 100 barrels of cranberries before overflowing. If a truck arrives and both the bins are full, the truck must wait until there is room in the bins. a. Draw the inventory build-up diagram. At what time do the trucks stop waiting?

b. At what time do the bins become empty?

c. What is the maximum number of barrels of cranberries that are waiting on the trucks?

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 processing rate increases to 125 barrels per hour. The seasonal workers would start working when trucks start to wait and finish working when the trucks stop waiting. At what time would ICU finish processing the cranberries using these seasonal workers?

Answer 1

Anwer a= Trucks arrive at a uniform rate over eight hours, from 6:00 a.m. until 2:00 p.m.

Bins are depleted at a rate of 100 barrels per hour, thus it will take 1 hour to load all 100 barrels

1400 + 1 hrs = 1500 or 3pm

Answer b= It will take another 1 hour until all the bins are empty because inventory depletes at 100 barrels per hour and the bins hold 00 barrels. Therefore, bins become empty at 4 p.m

Answer c= Number of barrels accumulate each hour is 150 – 100 = 50 barrels-

50 barrels * 8 hrs = 400 barrels

Maximum # of barrels waiting on trucks is 400 – 2*100 = 200 barrels