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Ás an engineer, suppose you are directed to design a pumping system to safely discharge a toxic industrial waste into a municipal reservoir. The concentrated wastewater from the plant will be mixed with freshwater from the lake, and this mixture is to be pumped into the center of the lake. You realize that the more water you mix with the waste, the more dilute it will be and thus the smaller the impact on the fish in the lake. On the other hand, the more the oou use, the more it costs in electricity for pumping. Your objective is to determine the optimum amount of water to pump so the overall cost is a minimum.

Ás an engineer, suppose you are directed to design a pumping system to safely discharge a toxic industrial waste into a municipal reservoir. The concentrated wastewater from the plant will be mixed with freshwater from the lake, and this mixture is to be pumped into the center of the lake. You realize that the more water you mix with the waste, the more dilute it will be and thus the smaller the impact on the fish in the lake. On the other hand, the more the oou use, the more it costs in electricity for pumping. Your objective is to determine the optimum amount of water to pump so the overall cost is a minimum.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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19. As an engineer, suppose you are directed to design a pumping system to safely discharge a plant will be mixed with freshwater from the lake, and this mixture is to be pumped into the center of the lake. You realize that the more water you mix with the waste, the more dilute toxic industrial waste into a municipal reservoir. The concentrated wastewater from the waten oc and thus the smaller the impact on the fish in the lake. On the other hand, the more the onou use, the more it costs in electricity for pumping. Your objective is to determine Cte optimum amount of water to pump so the overall cost is a minimum. Assume that the cost of pumping is given by the expression C, rday) depends on the pumping rate Q [gallons per minute, or gpm] of the water used 10 Q2. The cost C pump %3D pump to dilute the industrial waste. Now, suppose that some biologists have found that as more and more water dilutes the waste, the fish loss C [$/day] can be expressed as Csh = 2250 – 150 Q. fish With this information, construct a graph, with pumping rate on the abscissa showing the pumping cost, the fish-loss cost, and total cost on the ordinate. For the scale, plot 0 to 15 gallons per minute for flow rate. Determine both the minimum cost and the corresponding flow rate. Indicate the loca- tion of this answer on your graph.
Transcribed Image Text:19. As an engineer, suppose you are directed to design a pumping system to safely discharge a plant will be mixed with freshwater from the lake, and this mixture is to be pumped into the center of the lake. You realize that the more water you mix with the waste, the more dilute toxic industrial waste into a municipal reservoir. The concentrated wastewater from the waten oc and thus the smaller the impact on the fish in the lake. On the other hand, the more the onou use, the more it costs in electricity for pumping. Your objective is to determine Cte optimum amount of water to pump so the overall cost is a minimum. Assume that the cost of pumping is given by the expression C, rday) depends on the pumping rate Q [gallons per minute, or gpm] of the water used 10 Q2. The cost C pump %3D pump to dilute the industrial waste. Now, suppose that some biologists have found that as more and more water dilutes the waste, the fish loss C [$/day] can be expressed as Csh = 2250 – 150 Q. fish With this information, construct a graph, with pumping rate on the abscissa showing the pumping cost, the fish-loss cost, and total cost on the ordinate. For the scale, plot 0 to 15 gallons per minute for flow rate. Determine both the minimum cost and the corresponding flow rate. Indicate the loca- tion of this answer on your graph.
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