Consider a continuous operation in which raw green beans arrive to a processing unit. The green beans arrive at an average steady rate of 80 tons per hour from noon to 5 p.m. every day. The processing begins as soon as the beans start arriving, at noon. However, the processing unit can only process at a steady rate of 25 tons/hr. If need be, the processing unit can process for 24 hours a day. If beans arrive when the processing unit is busy, a queue of inventory will form.

a. [1 point] How many hours a day does the processing unit operate?

b. [1] What is the maximum inventory of unprocessed green beans?

c. [1] What is the capacity utilization of the processing unit? (Hint: This is equivalent to the fraction of a day the plant operates)

d. [2] How long on average does a bean stay in the queue? (Hint: First calculate average inventory(=AREA/T) and average throughput for the entire time the processing unit is operating. Then use little’s law to calculate CT.)