摘要新课标提出中学数学教育中要渗透数学探究、数学建模、数学文化这三个重要的内容，其中数学建模着重于让学生学会利用数学知识解决实际问题，逐步形成和发展数学应用意识，是极其重要的环节。

利用线性规划解决实际问题可以使学生接触数学建模的思想，增强应用意识，直观感受数学这一学科与日常生活的紧密联系。47792

  初等数学教育中不等式的内容，尤其在建立不等式方程组后，往往需要转换成高等数学中的线性规划问题。因此，对于不等式的解法研究就是线性规划问题的研究，有助于帮助教育工作者有针对性、有目的地帮助学生培养用线性规划解决代数问题的能力，引导学生学习理解线性规划的方法，培养培养学生数形结合、实践创新的思想

  此外，线性规划问题在小学奥数的统筹与规划问题中开始萌芽，在初中不等式的学习中初具雏形，最后集中被应用于高中不等式问题的解决。本文着重区分不同阶段，线性规划不同层次深度的体现，介绍学生学习掌握该知识点的要求，并最后对于简单线性规划的拓展给出新的意见和建议。

毕业论文关键词：线性规划； 初等数学； 教学； 不等式

Abstract

The new “high school mathematics curriculum standard” proposed to penetrate three important elements in secondary mathematics education, which include mathematics exploring, mathematical modeling and mathematical culture. Mathematical modeling focuses on letting students learn to use mathematical knowledge to solve practical problems, and gradually formed and developed awareness of the application of mathematics, which is an extremely important part.

Using linear programming to solve practical problems can let students contact with mathematical modeling, and enhance the awareness of application, feel that the discipline of mathematics is close contact with everyday life.

The content of inequalities in elementary mathematics, especially after the establishment of inequality equations, often needs to be converted into higher mathematics linear programming problem. Therefore, the study of the application of linear programming solution means research for the solution to middle school inequality, which is helpful for educators targeted purposefully to help students develop the ability to solve algebra problems using linear programming, also can develop students’ practice and innovation thinking.

In addition, the linear programming problem in elementary mathematical Olympiad began to sprout in and developed in junior high school , the final concentration was applied to inequality problem in high school. In this paper to distinguish the different stage, students learn to master the knowledge of the requirements, as well as for simple linear programming in the development and study how to guide students to understand the method of linear programming, finally，given the new idea to linear programming problem.

Keywords: linear programming; elementary mathematics; education ;  inequality

目录

1 研究背景和目的 3

2 线性规划问题及其数学模型 4

3 小学奥数中的统筹规划问题 5

4 中学数学中的不等式问题的简单介绍 6

4.1 初中阶段的不等式问题与线性规划 6

4.2 高中阶段线性规划的应用 7

4.2.1 利用平移找解法在可行域中进行求解 7

4.2.2 利用调整优值法求解 8

4.2.3 利用函数的单调性求解