有关于合理膳食问题的数学模型.doc

First compliance review of the application of the appraisal Committee, only through the compliance review of the application to take part in a detailed review. 8.1 application compliance review: does not meet one of the following conditions, procuratorial Agency to submit application through compliance reviews, be invalidated: (1) application of the formats, contents, meet the requirements of selected files, powers of Attorney, declarations by the legal representative and the tender agent application to meet the requirements; (2) licence and a bidding agent qualifications meet the requirements; (3) the similar project tendering agency agent number and provide proof of material compliance; (4) the tendering Agency intends to put into this project the number of professionals to meet the requirements; (5) are intended to the agent of the project as a project manager has similar projects the number of and references to meet the requirements; (6) no fraud case. 8.2 application review in detail the Evaluation Committee through compliance reviews will be selected for detailed review of the application. 8.2.1 tender agent institutions similar project tender performance requirements (16 points) tender agent institutions similar project tender performance 16 points, by two part composition (1) agent similar project of cumulative bid amount scored calculation rules for: Agent water project bid amount (on January 1, 2007 has has bid notice for associate) cumulative each reached 100 million Yuan have 2 points, water project cumulative bid amount scored up not over 6 points. In addition, completes a bid worth more than 500 million yuan in total 1 minute, but other items score accumulated winning amount up to a maximum of 6 points. (2) calculation rule for the number of agents similar projects: proxy bid amount (since January 1, 2007 winning notice shall prevail) bidding projects in more than 50 million Yuan by 2 points, but the Agency projects the number of scores up to 3 minutes. 8.2.2 to be agents of the construction project as a project manager in the same project performance (10 points) Project Manager agent performance scores including agents of the bidding agencies of similar projects, as well as in other similar project tendering agency service agent during performance. Total 10 Project Manager agent performance, made up of two parts (1) acting like the accumulated winning amount calculation rule: agents for water conservancy project bid amount (since January 1, 2007 winning notice for example) cumulative average reached 100 million Yuan 3 but scored no more than 5 minutes. (2) calculation rule for the number of agents similar projects: proxy bid amount (since January 1, 2007 winning notice for example) in the more than 50 million Yuan water conservancy project period of 3 minutes, but scores the number of agents similar projects up to a maximum of 5 points. Project Manager demonstrated to provincial-level and higher peoples Government or the development and Reform Commission published the winning bidder on the designated media publicity shall prevail. 8.2.3 staff requirement (25 points) 1, to the construction project serving personnel, 4 years experience in tendering agent, 2 points per person, 2 years experience in tendering agent .Pig is not a pig. With domestic international market and technology big environment of changes, as China traditional industry of pig production of job way and profit way are requirements related industry for resources integration, to quality security for premise, regulation based farming, and management cost and the production, and sales cost, go standardization, and scale, and intensive, and market road, fast upgrade whole industry chain of regulation capacity, market competition capacity and anti-risk capacity. First, industry analysis (a) the basic situation in China is a traditional hog production and consumption country, 2008 46.15 million tons of pork, pig stock 462.64 million head by the end pig slaughter 609.6 million. National pig industrys annual production value at around 650 billion yuan, nearly 50% per cent of annual output value of animal husbandry. Sichuan province in 2008 produced 6.52 million tons of pork, with 694,000 tons of Chengdu city, live pig sell 10.46 million, first 15 Vice-provincial cities in the country. The whole nation advantage regional planning (2008-2015) there are 437 counties (cities), 55, Sichuan, Chengdu has 7 (including in pengzhou). International pig industry mainly include the European Union, the United States, and Canada, and Brazil and other absolute scale of animal husbandry industry and technology developed countries. Market 1, the domestic market from Chinas meat consumption habits and economic analysis of the development situation, the emergence of new trends in the market of domestic pork and its products. Docking is a pig production and sales more closely. The Yangtze River Delta, Pearl River Delta and the Bohai rim economic developed area industrial structure adjustment gathered pace, two or three industries to the Central and Western bias. Second, the rigid domestic consumption growth. For a long period, pork is still the largest variety of meat consumption in China, the absolute consumption continues to grow. Especially in the vast rural market growth potential. Third, market for pork and higher product quality requirements. Pollution-free pork safety and health has shown a very good market prospects. Four is the market changing. Currently, cold meat, more and more varieties of meat and pork meat products, which accounted for a large proportion of pork consumption, stores, chain stores, supermarkets and other marketing methods is on the rise, and transport has been extended to more than 2000 km in RADIUS. Chengdu is an important River pig resource market, the citys commercial rate reaches above 60% of live pigs, pork and raw materials primary processing products in the domestic and international reputation is high. Western hog trading center in Chengdu and provides disease-free areas of construction in order to further accelerate the development of swine industry realizes space and conditions. 2, the international markets at present, annual volume of trade in live pigs in the world year around 18 million, about 6 million tons of pork trade. A large net exporter of pork is mainly the EU and North America,-importing countries mainly in Asia, Japan, and Korea, and Singapore, the Philippines, Hong Kong and other countries and regions, as well as Russia, about 3 million tonnes were imported. It is predicted that the world meat consumption increase of 80% in Asia in the future, our country has obvious geographical advantages, export potential. With the advancement of live pigs superiority industry belt construction, animal disease .有关于合理膳食问题的数学模型 摘 要 本文对平衡膳食问题进行了研究并建立该问题的数学模型。这是一个有关于平衡膳食的食谱类的数学模型，我运用lingo软件进行求解，求出了结果并进行了灵敏度分析，通过价格的变动的出来结论。约束优化，然后可应用Lingo软件中的函数模型来进行模型的建立，我们知道Lingo中一个完整的模型由集合定义、数据段、目标函数、和约束条件等组成。本文的合理膳食题也是一个与最优化问题差不多的问题，将其优化成为一个线性规划，以每日人们摄取营养物质最少来满足最低需求，营养物质每日的摄取量以题目给出的摄取量为约束条件来进行计算，以花费最少和摄取营养物质最高为目标函数。对这个多目标函数，我采用了熵值法将多个目标组合成了一个目标，通过表格的各种约束条件一一罗列出来，然后再进行求解。将模型优化为一个线性规划，最后讲求的结果再进行分析，最终得出结论。关键词：线性规划，lingo软件，目标函数一、问题重述某疗养院营养师要为某类病人拟订一周的菜单。可供选择的蔬菜及其费用和所含营养成分的数量以及这类病人每周所需各种营养成分的最低数量如表1.2所示。另外，为了口味的需要，规定一周内所用卷心菜不多于2份，其他蔬菜不多于4份。建立数学模型回答下列问题：（1）若病人每周需要14份蔬菜，问选用每种蔬菜各多少份，可使生活费用最小。（2）当市场蔬菜价格发生怎样波动时，你的模型仍然适用。表一所需费用营养物质蔬菜每份蔬菜所含营养成分费用（元/份）铁(mg)磷(mg)VA(单位)VC(mg)烟酸(mg)青豆0.451041580.31.5胡萝卜0.4528906530.351.5花菜1.05502550530.62.4卷心菜0.42575270.150.6甜菜0.5221550.251.8土豆0.57523580.81.0每周营养最低需求量6.0325175002455.0表述：这就是一个线性规划问题。现在随着人们社会生活水平的提高，进行合理搭配膳食也是越来越受到人们的重视，人类的食物是多种多样的。各种食物所含的营养成分不完全相同。除母乳外，任何一种天然食物都不能提供人体所需的全部营养素.平衡膳食必须由多种食物组成,才能满足人体各种营养需要，达到合理营养、促进健康的目的，因而要提倡人们广泛食用多种食物。只要对食物合理搭配,也就是每天膳食合理了,人体摄入的营养就会均衡了,也就是充分发挥了食物中的营养成份。人的营养需求就会合理的。因此本课题就是需要对人体摄取营养物质进行合理搭配。有题目可以运用lingo或者单纯形法都可以进行分析解答。二：问题分析：该问题是数学模型中的线性规划问题，根据题目所给的表格我们可以清晰的分析出一种最优化的方案。要求为了口味的需要，规定一周内所用卷心菜不多于2份，其他蔬菜不多于4份，这是本题目一个最基本的要求。再就是对表格具体进行分析，既要满足人们每周一个最合理的营养搭配，又要搭配这些食物的时候要花费的费用最小。在费用方面我们要求把每种蔬菜的价格以及所需量X相乘并进行相加，然后在需要的硬要物质方面，在把所有营养物质想家的时候一定要大于最低所需求的营养物质，对于x1,x2,x3,x4,x5,x6变量有一个具体的要求范围，进行合理的计算，如果在费用方面，在营养物质摄取方面计算的不合理就会导致费用超额，所以建立模型的过程当中就要慎重考虑这些问题，这是不可忽视的，也是建模过程能否成功的关键。在建立模型过程中我们需要引入一些变量，我们要注意变量值要为非负。3、 模型假设：1：假设每周营养物质供应充足，剩余部分并不能在供应。2：假设各类蔬菜不会出现疯狂的涨价和跌价情况出现，保证费用的合理。3：假设各类蔬菜所含的营养物质不会受到外界的影响，所含的营养物质不会变。4：保证每一周的费用够用，不会出现费用短缺。4、 符号约定假设各种蔬菜所需要的总费用为S青豆所需要的份数为X1；胡萝卜所需要的份数为X2；花菜所需要的份数为X3；卷心菜所需要的份数为X4；甜菜所需要的份数为X5；土豆所需要的份数为X6；蔬菜的量为Bi单价为Ci总费用为ais.t表二 蔬菜所需量总费用青豆X1S胡萝卜X2花菜X3卷心菜X4 甜菜X5土豆X65、 模型建立所求的值就是MIN，也就是最优化结果。求解：食谱问题的数学模型为：Mins=1.5*x1+1.5*x2+2.4*x3+0.6*x4+1.8*x5+1.0*x6;S.t=解释各个条件：第一个公式是铁的含量大于等于6.0mg0.45*x1+0.45*x2+1.05*x3+0.4*x4+0.5*x5+0.5*x6=6.0;第二个公式是磷的含量大于等于325mg10*x1+28*x2+50*x3+25*x4+22*x5+75*x6=325第三个公式是VA的含量大于等于17500415*x1+9065*x2+2550*x3+75*x4+15*x5+235*x6=17500;第四个公式是VC的含量大于等于2458*x1+3*x2+53*x3+27*x4+5*x5+8*x6=245;第五个公式是烟酸的含量大于等于5.00.3*x1+0.35*x2+0.6*x3+0.15*x4+0.25*x5+0.8*x6=5.0;第六个公式是卷心菜不多于2份其他各个蔬菜的份数小于等于4份x4=2;x1=4;x2=4;x3=4;x5=4;x6=6.0;10*x1+28*x2+50*x3+25*x4+22*x5+75*x6=325;415*x1+9065*x2+2550*x3+75*x4+15*x5+235*x6=17500;8*x1+3*x2+53*x3+27*x4+5*x5+8*x6=245;0.3*x1+0.35*x2+0.6*x3+0.15