A tomato processing plant for making tomato juice and tomato paste has the follo

Question

A tomato processing plant for making tomato juice and tomato paste has the following process. Trucks bring tomatoes from the fields, dump them into large bins, and return to the fields. Tomatoes flow from the bottom of the bins to a conveyor where they are continuously cleaned and chopped into a slurry. This slurry stream is divided according to a setting controlled by the plant manager into two streams (the proportion chosen according to current market demand), one that feeds the juice processor and one that feeds the paste concentrator. Output from both the juicer and the paste concentrator flow into the canning shed where they are packaged for shipment. In accordance with market demand, the plant manager has ordered that the plant make twice as much paste as juice each day. Due to long setup times in the separator equipment, this product mix must hold every minute of every day. The juicer can produce 100 gallons of juice in 5 minutes and the concentrator can produce 100 gallons of paste in 4 minutes. The cannery can package up to 2500 gallons per hour of product, be it juice or paste. What is the maximum processing rate, in gallons per hour, in the plant? Where is the bottleneck?

Explanation / Answer

Thr maximum processing rate in gallons = (100/5*60)+(100/4*60) or 2500 which is lower = 2700 or 2500 gallons which is lower = 2500 gallons.

Thr bottleneck is packing as it will result in not producing 200 gallons of juice or paste.

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