Consider a continuous operation in which raw tomatoes arrive to a processing unit in bulk. The tomatoes arrive at an average steady rate of 75 tons per hour from 8 a. m. to 1 p. m. every day. The processing begins as soon as the tomatoes start arriving, at 8 a. m. 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 tomatoes arrive when the processing unit is busy, a queue of inventory will form.
a. How many hours a day does the processing unit operate?
b. What is the maximum inventory of raw tomatoes?
c. What is the capacity utilization of the processing unit?
(Hint: This is equivalent to the fraction of a day the plant operates)
d. How long on average does a tomato stay in the queue?
(Hint: First calculate average inventory and average throughput for the entire time
the processing unit is operating. Then use little's law to calculate CT.)
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