调试Matlab程序、 Mathematical Modeling作业代做留学生、代写Mathematical Modeling

Instruction: Submit your answers and codes to SEPARATE links on iSpace. Late orincorrect submissions will not be graded. Each question carries the same weight.1. (Mixing tanks) Two very large tanks A and B are each partially lled with 100 gallons ofbrine. Initially, 100 pounds of salt is dissolved in the solution in tank A and 50 poundsof salt is dissolved in the solution in tank B. The system is closed in that the well-stirredliquid is pumped only between the tanks, as shown in Figure 1.Figure 1: Container within a container.(a) Use the information given in the gure to construct a mathematical model for thenumber of pounds of salt x1(t) and x2(t) at time t in tanks A and B, respectively.(b) Find a relationship between the variables x1(t) and x2(t) that holds at time t.Explain why this relationship makes intuitive sense. Use this relationship to helpnd the amount of salt in tank B at t = 30 min.2. (Newton’s Law of cooling/warming) As shown in Figure 2, a small metal bar is placedinside container A, and container A then is placed within a much larger container B. Asthe metal bar cools, the ambient temperature TA(t) of the medium within container Achanges according to Newton’s law of cooling. As container A cools, the temperature ofthe medium inside container B does not change signi cantly and can be considered to bea constant TB. Construct a mathematical model for the temperatures T(t) and TA(t),where T(t) is the temperature of the metal bar inside container A. Find a solution ofthe system subject to the initial conditions T(0) = T0, TA(0) = T1. (Assume here thatthe temperature, T(t), of the metal bar does not a ect the temperature, TA(t), of themedium in container A)Figure 2: Container within a container.3. (Electoral system / Voting theory) An electoral system is the system that determines howelections and referendums take place and how their results are arrived at. Di erent rulesof voting may sometimes lead to di erent winner(s) even if the preferences of constituentsremain the same.Consider the following voting rules (assume only a single winner)1. Plurality method: A single round of election is held. The candidate who polls themost among their counterparts is elected.2. Single runo method: A preliminary round of election is held and two candidateswho receive the most number of votes advance to the nal round. The nal roundis then based on the plurality method. The winner of the nal round is chosen asthe elect.3. Instant runo method: Multiple rounds of election are held. In each round, thecandidate who receive the least number of votes is eliminated. When there are onlytwo candidates remaining, use the plurality method to determine the elect.4. Coombs method: Multiple rounds of election are held. In each round, the con-stituents are required to rank every candidate in terms of their preferences. Thecandidate who received the most number of votes for the last place is eliminated.When there are only two candidates remaining, use the plurality method to determinethe elect.5. Borda count: A single round of election is held. The constituents are requiredto rank every candidate in terms of their preferences. For each vote casted, thecandidate in the last place gets 1 mark, the candidate in the second last place gets2 marks, ..., the candidate in the rst place gets n marks (n is the total number ofcandidates). The candidate who gets the highest mark is the elect.(a) Consider the following voting results from 30 students on their favourite sports team.There are 4 teams and each student ranks them from the rst (most like) and thefourth (least like). For example, 11 students vote B as the rst, D as the second, Cas the third and A as the fourth. Assume that the voters’ preferences do not changeif multiple rounds of voting are necessary. For each voting rule above, determine thewinner.Votes 11 10 9First B C ASecond D D DThird C A CFourth A B B(b) Investigate the 2002 French presidential election. Which rule was used? Write anote to discuss the e ect if 1% of all voters for Jean-Marie Le Pen instead votedfor Jacques Chirac in the rst round (other votes remain unchanged - see the tablesbelow).You will need to get additional information on your own to draw the conclusion.Table 1: Real result ( rst round)Candidate % RankJacques Chirac 19.88% 1Jean-Marie Le Pen 16.86% 2Lionel Jospin 16.18% 3... ...Table 2: Hypothesised result ( rst round)Candidate % RankJacques Chirac 20.88% 1Lionel Jospin 16.18% 2Jean-Marie Le Pen 15.86% 3... ...4. (Secretary problem / Marriage problem) Use simulation to demonstrate the secretary/marriageproblem (refer to case study 5) with N = 10 and N = 50 candidates, respectively. Foreach N, obtain the probability that the best candidate is chosen pN(k) for k = 1;2;:::N.For each value of k, perform. su cient number of independent runs such that the 95%con dence interval with Ur 0:01 is obtained for pN(k). Use your simulation results toplot a gure (see Figure 3 as an example, the vertical error bar at each point representscon dence interval) to illustrate the relationship between k and pN(k).For more information, see: https://en.wikipedia.org/wiki/Secretary_problem or本团队核心人员组成主要包括BAT一线工程师，精通德英语！我们主要业务范围是代做编程大作业、课程设计等等。我们的方向领域：window编程 数值算法 AI人工智能 金融统计 计量分析 大数据 网络编程 WEB编程 通讯编程 游戏编程多媒体linux 外挂编程 程序API图像处理 嵌入式/单片机 数据库编程 控制台 进程与线程 网络安全 汇编语言 硬件编程 软件设计 工程标准规等。其中代写编程、代写程序、代写留学生程序作业语言或工具包括但不限于以下范围:C/C++/C#代写Java代写IT代写Python代写辅导编程作业Matlab代写Haskell代写Processing代写Linux环境搭建Rust代写Data Structure Assginment 数据结构代写MIPS代写Machine Learning 作业 代写Oracle/SQL/PostgreSQL/Pig 数据库代写/代做/辅导Web开发、网站开发、网站作业ASP.NET网站开发Finance Insurace Statistics统计、回归、迭代Prolog代写Computer Computational method代做因为专业，所以值得信赖。如有需要，请加QQ：99515681 或邮箱：[email protected] 微信：codehelp QQ：99515681 或邮箱：[email protected] 微信：codehelp