Linear Programming
The harvest of cane sugar in Australia is highly mechanized. The sugar cane is immediately transported to a sugar house in wagons that run on a network of small rail tracks. The sugar content of a wagon load depends on the field it has been harvested from and on the maturity of the sugar cane. Once harvested, the sugar content decreases rapidly through fermentation and the wagon load will entirely lose its value after a certain time. At this moment, eleven wagons all loaded with the same quantity have arrived at the sugar house. They have been examined to find out the hourly loss and the remaining life span (in hours) of every wagon; these data are summarized below:
Every lot may be processed by any of the three, fully equivalent production lines of the sugar house. The processing of a lot takes two hours. It must be finished at the latest at the end of the life span of the wagon load.
The manager of the sugar house wishes to determine a production schedule for the currently available lots that minimizes the total loss of sugar. Ensure that you display only when each wagon is unloaded and the loss of product from each wagon in each unloading period.
Please I need a Linear Program to determine a production schedule for this problem any help is appreciated thanks!
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