This problem involves minimization with mixed constraints. Three water purification facilities can handle at most 15 million gallons in a certain time period. Plant I leaves 20% of certain impurities and costs $10,000 per million gallons. Plant II leaves 15% of these impurities and costs $30,000 per million gallons. Plant III leaves 10% impurities and costs $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 12 million gallons, find the number of gallons each plant should handle to achieve the desired level of purity at minimum cost.

Plant I		million gallons
Plant II		million gallons
Plant III		million gallons

Find the minimum cost. $

Johnson City Cooperage manufactures 30-gallon and 55-gallon fiber drums. Each 30-gallon drum takes 30 minutes to make, each 55-gallon drum takes 40 minutes to make, and the company has at most 9,000 minutes available each week. Also, workplace limitations and product demand indicate that the number of 55-gallon drums produced plus half the number of 30-gallon drums produced should be at least 80, and the number of 30-gallon drums should be at least twice the number of 55-gallon drums. If Johnson City Cooperage's manufacturing costs are $3 for each 30-gallon drum and $4 for each 55-gallon drum, how many of each drum should be made each week to satisfy the constraints at minimum cost? 30-gallon drums 55-gallon drums Find the minimum cost. $