Three water purification facilities can handle at most 17 million gallons in a certain time period. Plant I leaves 20% of certain impurities and costs $30,000 per million gallons. Plant II leaves 15% of these impurities and costs $40,000 per million gallons. Plant III leaves 10% impurities and costs $50,000 per million gallons. The desired level of impurities in the water from all three plants is at most 15%. If Plant I and Plant III combined must handle at least 14 million gallons, find the number of gallons each plant should handle to achieve the desired level of purity at minimum cost.

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