Chapter 4.5, Problem 35E

Problems 31-36 involve minimization with mixed constraints.

Water purification Three water purification facilities can handle at most 10 million gallons in a certain time period. Plant I leaves 20% of certain impurities and costs $20,000 per million gallons. Plant II leaves 15% of these impurities and costs $30,000 per million gallons. Plant III leaves 10% impurities and costs $40,000 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 6 million gallons, find the number of gallons each plant should handle to achieve the desired level of purity at minimum cost. Find the minimum cost.