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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 管理科学代写|决策论代写Management Science Models for Decision Making代考|The Importance of LP

LP has now become a dominant subject in the development of efficient computational algorithms, in the study of convex polyhedra, and in algorithms for decision making. But for a short time in the beginning, its potential was not well recognized.
Dantzig tells the story of how when he gave his first talk on LP and his simplex method for solving it, at a professional conference, Hotelling (a burly person who liked to swim in the sea, the popular story about him was that when he does, the level of the ocean raises perceptibly, see Figs. $1.1$ and 1.2; my thanks to Katta Sriramamurthy and Shantisri Katta for these figures) dismissed it as unimportant since everything in the world is nonlinear. But Von Neumann came to the defense of Dantzig saying that the subject will become very important; see Page xxvii of Dantzig and Thapa (1997). The preface in this book contains an excellent account of the early history of LP from the inventor of the most successful method in OR and in the mathematical theory of polyhedra.

Von Neumann’s early assessment of the importance of LP turned out to be astonishingly correct. Today, the applications of LP in almost all areas of science are so numerous, so well known, and recognized that they need no enumeration. Also, LP seems to be the basis for most of the efficient algorithms for many problems in other areas of mathematical programming. Many of the successful approaches in nonlinear programming, discrete optimization, and other branches of optimization are based on LP in their iterations. Also, with the development of duality theory and game theory (Gale 1960), LP has also assumed a central position in economics.

## 管理科学代写|决策论代写Management Science Models for Decision Making代考|Marginal Values and Other Planning Tools that can be Derived from the LP Model

We will illustrate the very useful planning information that can be derived from an LP model for a real-world decision-making problem, using the example of the fertilizer maker’s product mix problem discussed in Example 3.4.1 of Sect. $3.4$ of Murty (2005b), referred to earlier in Sect. 1.3.1.The fertilizer maker (FM) produces Hi-ph, Lo-ph fertilizers using three raw materials, RM-1, 2, 3 as inputs, whose supply is currently limited. Here is all the data on the problem.

So the total production cost/ton of Hi-ph $=$ (input raw material costs) $+$ (other production costs) $=2 \times 50+1 \times 75+1 \times 60+50=285 \$ /$ton, and since its market price is$\$300$, production of Hi-ph leads to a net profit of 300-285=\$$15 / ton made. The net profit from Lo-ph of \ 10 / ton is computed in the same way. The market is able to absorb all the Hi-ph, Lo-ph fertilizers the company can produce, and so at present there is no limit on the production levels of these fertilizers. Defining x_1, x_2= tons of Hi-ph, Lo-ph produced daily, the LP model for maximizing the company’s daily net profit is$$ \begin{aligned} \text { Maximize } z(x)=15 x_1+10 x_2 & \ \text { s. to } 2 x_1+x_2 & \leq b_1=1500 \quad \text { (RM-1 availability) } \ x_1+x_2 & \leq b_2=1200 \quad \text { (RM-2 availability) } \ x_1 & \leq b_3=500 \quad \text { (RM-3 availability) } \ x_1, x_2 & \geq 0 . \end{aligned} $$The constraint 2 x_1+x_2 \leq 1500 requires that the feasible region of this problem should be on the side of the straight line \left{x: 2 x_1+x_2 \leq 1500\right} in Fig. 1.3. Likewise, all other constraints in (1.9) can be represented by the corresponding half-spaces in Fig. 1.3, leading to the set of feasible solutions, K of this problem as the shaded region in Fig. 1.3. Selecting any feasible solution, x^0=0 say, we draw the objective line {x : \left.z(x)=z\left(x^0\right)\right} through it, and then move this objective line parallel to itself, increasing the RHS constant in its representation as far as possible (because in this problem we need to maximize the value of z(x) ), while still maintaining a nonempty intersection with the feasible region. If \hat{z} is the final value of the RHS constant in this process, then \hat{z} is the maximum value of z(x) in the problem, and any point in the intersection of {z(x)=\hat{z}} \cap K is an optimum solution of (1.9). # 决策论代写 ## 管理科学代写|决策论代写管理科学的决策模型代考| LP的重要性 . LP现已成为高效计算算法的发展、凸多面体的研究和决策算法的主导课题。但在开始的很短一段时间内，它的潜力没有得到充分认识。Dantzig讲述了他如何在LP上做第一次演讲，以及他如何用单纯形方法解决它的故事，在一次专业会议上，Hotelling(一个身材魁梧的人，喜欢在海里游泳，关于他的流行故事是，当他这样做时，海洋的高度会明显上升，见Figs。1.1和1.2;我感谢Katta Sriramamurthy和Shantisri Katta提供这些数据)认为它不重要，因为世界上的一切都是非线性的。但冯·诺伊曼为丹齐格辩护说这个主题将变得非常重要;参见《丹齐格和塔帕》(1997)第xxvii页。这本书的序言包含了从OR和多面体数学理论中最成功的方法的发明者的LP的早期历史的精彩叙述 冯·诺伊曼早期对LP重要性的评估被证明是惊人的正确。今天，LP在几乎所有科学领域的应用都是如此之多，如此之广为人知，并且得到认可，无需赘述。此外，LP似乎是数学规划其他领域的许多问题的大多数有效算法的基础。在非线性规划、离散优化和其他优化分支中，许多成功的方法都是基于LP的迭代。此外，随着对偶理论和博弈论的发展(Gale 1960)， LP也在经济学中占据了中心地位 ## 管理科学代写|决策论代写用于决策的管理科学模型代考|从LP模型中派生的边际值和其他规划工具 我们将使用Murty (2005b)的3.4节的例3.4.1中讨论的化肥制造商的产品组合问题的例子，说明可以从LP模型中导出的非常有用的规划信息，这些规划信息用于现实世界的决策问题。化肥生产商(FM)生产高ph值，低ph值化肥使用三种原料，RM-1, 2,3作为投入，其供应目前是有限的。这是关于这个问题的所有数据。 所以每吨Hi-ph的总生产成本=(输入原材料成本)+(其他生产成本)=2 \times 50+1 \times 75+1 \times 60+50=285 \ /吨，由于其市场价格为\ 300，生产Hi-ph的净利润为300-285=\$$15 /$吨。Lo-ph为$\$10 /$吨的净利润也用同样的方法计算。市场能够吸收该公司生产的所有高ph值、低ph值化肥，因此目前对这些化肥的生产水平没有限制。定义每天生产的Hi-ph, Lo-ph为$x_1, x_2=$吨，公司日净利润最大化的LP模型为
\begin{aligned} \text { Maximize } z(x)=15 x_1+10 x_2 & \ \text { s. to } 2 x_1+x_2 & \leq b_1=1500 \quad \text { (RM-1 availability) } \ x_1+x_2 & \leq b_2=1200 \quad \text { (RM-2 availability) } \ x_1 & \leq b_3=500 \quad \text { (RM-3 availability) } \ x_1, x_2 & \geq 0 . \end{aligned}

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MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

assignmentutor™您的专属作业导师
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