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# 数学代写|线性规划代写Linear Programming代考|Mathematical Model

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## 数学代写|线性规划代写Linear Programming代考|Mathematical Model

The implementation of some linear programming methods in the MATHEMATICA programming language can be found in [5]. The General form of linear programming problems can be expressed as follows. Determine the values of the variables $y_1, \ldots, y_k$ that match linear equations the inequalities
\begin{aligned} & N_i^{(1)}: \sum_{j=1}^k a_{i j} y_j \leq \beta_i, \quad i \in I_1 \ & J_i: \sum_{j=1}^k a_{i j} y_j=\beta_i, \quad i \in I_2 \ & N_i^{(2)}: \sum_{j=1}^k a_{i j} y_j \geq \beta_i, \quad i \in I_3 \ & y_j \geq 0, \quad j \in J \subseteq{1, \ldots, k}, \end{aligned}

where $I_1 \cup I_2 \cup I_3={1, \ldots, m}, I_1 \cap I_2=\emptyset, I_1 \cap I_3=\emptyset, I_2 \cap I_3=\emptyset$, so that the linear objective function
$$\omega(y)=\omega\left(y_1, \ldots, y_k\right)=\gamma_1 y_1+\cdots+\gamma_k x_k$$
has an extremum, i.e., minimum or maximum. They are $\alpha_{i j}, \beta_i, \gamma_j$ known real numbers.

By convention, in the general case, a vector $y \in \mathbb{R}^k$ represents the $k$ – tuple of real numbers $y=\left(y_1, \ldots, y_k\right)$,, while matrix formulas imply that $y$ is a matrix of type $k \times 1$ (vector), i.e.:
$$y=\left[\begin{array}{c} y_1 \ \vdots \ y_k \end{array}\right], \quad y^\tau=\left[y_1 \ldots y_k\right]$$

## 数学代写|线性规划代写Linear Programming代考|Properties of a Set of Constraints

Let the linear programming problem be given in the standard format (1.5.0. 4). The set $\Gamma_P={y \mid A y=\beta, y \geq 0}$ on which the function $\omega$ is essentially defined influences extreme values and has interesting geometric properties. Below, we assume that $r=m<n$, where $m$ and $n$ are dimensions matrix $A$, and $r$ is its rank. Then the system has infinitely many solutions so it makes sense to seek extreme value functions $\omega(y)$ defined on the set $\Gamma_P$. Label the columns of the matrix $A$ as $K_1, \ldots, K_n$.
Note that the vectors $K_1, \ldots, K_n$, and $\beta$ are dimensions of $m$.
Recall that the vectors $y_1, \ldots, y_n$ are linearly independent if it follows from the equation $\alpha_1 y_1+\cdots+\alpha_n y_n=0 \alpha_1=\cdots=\alpha_n=0$, otherwise they are linearly dependent. Form expression $a=\sigma a^1+$ $(1-\sigma) a^2, 0 \leq \sigma \leq 1$ is called the convex combination of vectors $a^1$ and $a^2$. Generally a convex combination of vectors $a^1, \ldots, a^k$ is any vector of $a$ forms:
$$a=\sum_{i=1}^k \sigma_i a^i, \quad \sum_{i=1}^k \sigma_i=1, \quad\left(\sigma_1, \ldots, \sigma_k \geq 0 .\right)$$
The set of vectors $K$ is convex if:
$$\left(\forall a^1, a^2 \in K\right)\left(\sigma a^1+(1-\sigma) a^2 \in K, \quad 0 \leq \sigma \leq 1\right) .$$

## 数学代写|线性规划代写Linear Programming代考|Mathematical Model

\begin{aligned} & N_i^{(1)}: \sum_{j=1}^k a_{i j} y_j \leq \beta_i, \quad i \in I_1 \ & J_i: \sum_{j=1}^k a_{i j} y_j=\beta_i, \quad i \in I_2 \ & N_i^{(2)}: \sum_{j=1}^k a_{i j} y_j \geq \beta_i, \quad i \in I_3 \ & y_j \geq 0, \quad j \in J \subseteq{1, \ldots, k}, \end{aligned}

$$\omega(y)=\omega\left(y_1, \ldots, y_k\right)=\gamma_1 y_1+\cdots+\gamma_k x_k$$

$$y=\left[\begin{array}{c} y_1 \ \vdots \ y_k \end{array}\right], \quad y^\tau=\left[y_1 \ldots y_k\right]$$

## MATLAB代写

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。