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The Dairy Farmers of Ontario Organization schedules milk collection from farmers in Ontario every morning. A truck stops by at Norbert's farm at 8:30am in the morning. Farmer Norbert starts to milk his 108 cows every morning at 5am. It takes him 5 minutes to milk a single cow. The cow will give 15 litres of milk. (The same process repeats in the afternoon at 5pm but we are only interested in the morning. Note: A cow can only be milked once in the morning!) Norbert has three milking machines that he can operate at the same time, so he can milk three cows in parallel. The milk will be collected in a cooling tank (of sufficient size) until the milk truck comes to pick it up. The truck's pump can pump out 81 litres per minute from Norbert's tank.
(a) Starting at 5:00am, draw an inventory build up diagram that shows the amount of milk in the Norbert's storage tank. What is the average tank inventory? Provide your solution with two decimal places.
(b) Calculate the average system throughput rate. Provide your solution with two decimal places.
(c) To make sure that the milk meets the high quality standards of the Dairy Farmers of Ontario, they want to know the average time the milk spends in Norbert's storage tank. Provide your solution with three decimal places. (in hours)
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