Three factories each dump waste water containing three different types of pollutants into a river. State regulations require the factories to treat their waste in order to reduce pollution levels. The following table shows the possible percent reduction of each pollutant at each site and the cost per ton to process the waste.

If the state requires a reduction of at least 65 tons per day of pollutant 1, at least 40 tons per day of pollutant 2, and at least 20 tons per day of pollutant 3, find the number of tons of waste that must be treated each day at each site so that the state's requirements are satisfied and the treatment costs are minimized. Find the minimum cost.
Use the simplex method, Excel, or some other technology.

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Factory 2 45% Factory 1 Factory 3 Pollutant 1 Pollutant 2 Pollutant 3 20% 15% 5% 75% 65% 10% 30% 15% Cost/ton $20 $8 $50