Suppose that each day, northern, central and southern California each use 100 billion gallons of water. Also assume that northern California and central California have available 120 billion gallons of water, while southern California has 40 billion gallons of water available. The cost of shipping one billion gallons of water between the three regions is as follows:
Northern Central Southern
Northern $5,000 $7,000 $10,000
Central $7,000 $5,000 $6,000
Southern $10,000 $6,000 $5,000
We will not be able to meet all demand for water, so we assume that each billion gallons of unmet demand incurs the following shortage costs:
Northern Central Southern
Storage cost/billion $6,000 $5,000 $9,000
gallon short
How should California's water be distributed to minimize the sum of shipping and shortage costs?
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