摘要运筹学中有一个重要的分支，是线性规划，是辅助人们科学的对日常生活与工作进行管理的一种数学方法。本篇论文主要讨论运筹学中线性规划在实际生活中的应用。

线性规划问题的求解，是从满足的约束条件中找出一个解，使其目标函数达到最大值，应用在实际生活中一般用来求取最优方案、最高效率等。线性规划问题的解题方法包括了单纯形法、改进单纯形法、对偶单纯形法、原始对偶方法、分解算法和各种多项式时间算法等。51483

单纯形法是用于求解线性规划问题的基本方法。后来为了改进单纯形法每次迭代中积累起来的进位误差，改进单纯形法被提出，基本步骤和单纯形法大致相同，减少迭代中的累积误差，提高计算精度，同时也减少了在计算机上的存储量。除此之外为了提高解题速度，还产生了对偶单纯形法、原始对偶方法、分解算法和各种多项式时间算法，在此不作描述，正文中会选取部分进行大致的描述。

不过，在面对只有两个变量的线性规划问题时，我们也可以采用图解法进行求解。该方法需要建立坐标系，将约束条件在图上表示；确立满足条件的解的范围；绘制出目标函数的图形，最终确定最优解。这种方法的特点是直观而易于理解，但实用价值不大。

基于对现实生活中问题的考虑，将复杂因素进行了简单化，选取了两个实例使用线性规划的方法进行求解，分别采用了图解法和单纯形法。

There is an important branch of operations research, which is a kind of mathematical method for the management of daily life and work. This paper mainly discusses the application of linear programming in the practical life.

The solution of the linear programming problem is to find a solution to satisfy the constraint conditions, so that the objective function can reach the maximum value, and the application in real life is generally used to obtain the optimal scheme, the maximum efficiency and so on. The solution methods of linear programming include simplex method, modified simplex method, dual simplex method, primal dual method, decomposition algorithm and various polynomial time algorithm.

The simplex method is a basic method for solving linear programming problems. Later in order to improve at each iteration, the simplex method and the accumulated rounding error, improved simplex method is proposed, and the basic steps of the simplex method is roughly the same as in, reduce the accumulated error iteration, improve the calculation accuracy, but also reduce the amount of storage on a computer. In addition to increase the speed of solving problems, also produced dual simplex method, primal dual methods, decomposition algorithm and polynomial time algorithm, here is not described, the text will select part of a general description.

However, in the face of a linear programming problem with only two variables, we can also be solved by the graphical method. This method needs to establish the coordinate system, the constraints are shown in the diagram; the establishment to meet the conditions of the scope of the solution; draw out the objective function of the graphics, and ultimately determine the optimal solution. This method is intuitive and easy to understand, but little practical value.

The problems in real life based on the consideration of the complex factors were simple, selects two instances of the use of linear programming to solve the graphic method and simplex method.

毕业论文关键词：线性；图解法；单纯形法；最优解；可行解；目标函数；可行域；基变量；换基迭代；矩阵

Keyword: Linear；Graphic Method；Simplex Method；Optimum Solution；Feasible Solution；Objective Function；Feasible Region；Base Variable；Change Basis Iteration；Matrix.