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1、 Team # 20617 Page 1 of 19 For office use only T1 _ T2 _ T3 _ T4 _ Team Control Number 20617 Problem Chosen B For office use only F1 _ F2 _ F3 _ F4 _ 2013 Mathematical Contest in Modeling (MCM) Summary Sheet (Attach a copy of this page to your solution paper.) Type a summary of your results on this
2、page. Do not include the name of your school, advisor, or team members on this page. Summary China will face very serious shortage of water in 2025 due to physical scarcity and rapid growth of economic and population. In view of this fact, we develop a strategy to help defuse the water crisis. At fi
3、rst, we build a linear regression model to make a prediction about the water consumption of each province and the whole country in 2025, and analyze the coefficient of determination to prove that the model can predict efficiently. Then we analyze the water problem at the province level and the natio
4、nal level. In order to solve the canal-line problem in water transfer, all the provinces are divided into 5 levels according to the water shortage degree. Then we build a network model regarding each province as a node. So the canal-line problem is transformed to a minimum spinning tree (MST) proble
5、m. With the optimized canal-lines, we estimate the cost of the whole project according to the experiences of South-to-North water diversion. In the rest of the content, we shift from the province level to national. In order to relieve the over-use of groundwater, decrease the pollution and help reli
6、eve the water shortage, we suggest 3 ways to supply fresh water, including water desalinization, water purification and water storage. We estimate the plant construction cost of water desalinization according to the historical data, which helps to make evaluation among the 3 methods for the ultimate
7、 strategy. The 4th model is built to estimate the cost of water purification in detail. The model helps to calculate the average cost of sewage recycling in China with the consideration of electric power charge, chem- ical agent charge, maintenance charge and other charges. We also estimate the tota
8、l cost of constructing a reservoir according to the history experiences rough- ly to help determine the ultimate strategy. Finally, we build a model to give consideration to all the three methods above with the help of rank sum ratio (RSR) method. The RSR method has an excellent feature that it tran
9、sforms samples into Team # 20617 Page 2 of 19 non-dimensional statistics. With the help of the final model, we are able to come up with an opti- mized strategy. Content 1. Introduction . 3 2. General assumptions . 3 3. Linear model to predict the water withdrawal . 3 3.1 Symbols and explanations . 3
10、 3.2 Model and calculation . 4 3.3 Analysis of variance . 6 3.3 Strength and weakness . 7 4. Model for water transfer among provinces . 7 4.1 Symbols and explanations . 7 4.2 Model and calculation . 8 4.3 Strength and weaknesses. 10 4.4 Impact . 10 5. Analysis of national level. 11 6. Model for water Desalinization . 11 6.1 Assumptions for model 3 . 11 6.2 Symbol and explanations . 12 6.3 Model and calculation .
