Solving Markov Chain Problem for Water Distribution Co. in California

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SUMMARY

The discussion focuses on modeling a water distribution problem in southern California using a Markov Chain. The water distribution company receives 3 million gallons (MG) of water monthly and can store up to 4 MG. The monthly usage in Orange County is probabilistic, with defined probabilities for usage levels of 1 MG, 2 MG, 3 MG, and 4 MG. The challenge lies in defining the states of the Markov Chain to accurately represent the varying water levels and sales to agricultural distributors.

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A water distribution company in southern California gets its water supply from the north and sell it back to its customers in Orange county. Assume the following simplified scheme: 3 MG (millions of gallons) of water arrives from the north at the beginning of the month. The company can store up to 4 MG. If it has any excess beyond that, it sells it immediately to another distributor for agricultural usage. The monthly usage in Orange county varies randomly: it is

1 MG with probability .2
2 MG ” ” .3
3 MG ” ” .4
4 MG ” ” .1

I need to set up a Markov Chain to model this problem, but I can't think of a way to define the states. Any ideas?
 
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What are the possible amounts of water the distributor has?
 

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