A metal refining factory has a waste disposal problem. For 1 kg of metal produced, 3...

  

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A metal refining factory has a waste disposal problem. For 1 kg of metal produced, 3 kg of waster are created. The waste is contained in wastewater at a concentration of 2 kg/m3. The regulatory authority has imposed an effluent maximum standard of 100,000 kg/week that the company may discharge into a nearby river. The factory has a production capacity of 55,000 kg of metal per week. Metal is sold at a price of $1.30/kg and production costs are $0.90/kg. The factory's wastewater treatment facility has a maximum capacity of 70,000 m3/week, however the facility's efficiency (fraction of waste removed) varies with the waste loading. If W is the wastewater inflow in 104 m3/week, then for W between 0-70,000 m3/week, the treatment efficiency is 1-0.06*W. Thus more wastewater in the treatment plant means less efficiency at removing the waste. Wastewater treatment costs are $0.20/m3. Refined metal Untreated wastewater Treated wastewater Factory Wastewater Treatment plant System boundary The metal factory needs to meet two objectives: Obj. 1: discharge no more than 100,000 kg/week of waste into the river Obj. 2: maximize profits ($/week) Consider the following alternatives: 1. For a production of 50,000 kg/week of metal and treatment of 100,000 kg/week of waste in the treatment plant, does this meet both objectives? What are the expected total effluent (kg/week) to the river and the total profits ($/week)? 2. Suppose the metal factory decides to prioritize minimizing waste to the river, but still needs to be profitable to cover labor, etc. (profit > $1000/week.) How much metal can they produce and how much effluent to the river is this? Set up this problem (equations) and describe how you would solve it. Bonus points for solving. 3. Suppose the metal factory decides to prioritize maximizing profits, but cannot exceed effluent standards. How much metal can they produce and what is the total profit? Set up this problem (equations) and describe how you would solve it. Bonus points for solving. River A metal refining factory has a waste disposal problem. For 1 kg of metal produced, 3 kg of waster are created. The waste is contained in wastewater at a concentration of 2 kg/m3. The regulatory authority has imposed an effluent maximum standard of 100,000 kg/week that the company may discharge into a nearby river. The factory has a production capacity of 55,000 kg of metal per week. Metal is sold at a price of $1.30/kg and production costs are $0.90/kg. The factory's wastewater treatment facility has a maximum capacity of 70,000 m3/week, however the facility's efficiency (fraction of waste removed) varies with the waste loading. If W is the wastewater inflow in 104 m3/week, then for W between 0-70,000 m3/week, the treatment efficiency is 1-0.06*W. Thus more wastewater in the treatment plant means less efficiency at removing the waste. Wastewater treatment costs are $0.20/m3. Refined metal Untreated wastewater Treated wastewater Factory Wastewater Treatment plant System boundary The metal factory needs to meet two objectives: Obj. 1: discharge no more than 100,000 kg/week of waste into the river Obj. 2: maximize profits ($/week) Consider the following alternatives: 1. For a production of 50,000 kg/week of metal and treatment of 100,000 kg/week of waste in the treatment plant, does this meet both objectives? What are the expected total effluent (kg/week) to the river and the total profits ($/week)? 2. Suppose the metal factory decides to prioritize minimizing waste to the river, but still needs to be profitable to cover labor, etc. (profit > $1000/week.) How much metal can they produce and how much effluent to the river is this? Set up this problem (equations) and describe how you would solve it. Bonus points for solving. 3. Suppose the metal factory decides to prioritize maximizing profits, but cannot exceed effluent standards. How much metal can they produce and what is the total profit? Set up this problem (equations) and describe how you would solve it. Bonus points for solving. River

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