linear programming

简明释义

线性规划

英英释义

例句

1.The logistics team implemented linear programming to improve delivery routes.

物流团队实施了线性规划以改善配送路线。

2.Many airlines utilize linear programming for scheduling flights and crew assignments.

许多航空公司利用线性规划来安排航班和机组人员分配。

3.By applying linear programming, we can minimize costs while maximizing output.

通过应用线性规划，我们可以在最大化产出的同时最小化成本。

4.The company used linear programming to optimize its production schedule.

公司使用线性规划来优化其生产计划。

5.Using linear programming, the farm was able to allocate resources more efficiently.

通过使用线性规划，农场能够更有效地分配资源。

作文

Linear programming is a mathematical method used for optimizing a particular outcome, such as maximizing profit or minimizing cost, subject to certain constraints. This technique has a wide range of applications in various fields, including economics, engineering, military operations, and transportation. The core idea behind linear programming (线性规划) is to find the best possible solution from a set of feasible solutions that satisfy all given constraints. To better understand linear programming (线性规划), it is essential to break down its components. First, we need to define the objective function, which represents the goal we want to achieve. For example, a company may want to maximize its profits based on the number of products produced. The objective function is usually expressed as a linear equation. Next, we have the constraints, which are the limitations or requirements that must be met. These can include resource availability, production capacity, and market demand. Each constraint can also be represented as a linear equation or inequality. The feasible region, which is the area where all constraints overlap, is crucial in linear programming (线性规划) because it contains all the possible solutions that meet the specified conditions. The graphical method is one way to visualize linear programming (线性规划). By plotting the objective function and constraints on a graph, we can identify the feasible region and determine the optimal solution. However, this method is limited to problems with two variables. For more complex problems involving more than two variables, other techniques such as the Simplex method or interior-point methods are employed. One practical application of linear programming (线性规划) is in the transportation industry. Companies often face the challenge of minimizing shipping costs while meeting delivery schedules and customer demands. By using linear programming (线性规划), they can optimize their routes, allocate resources efficiently, and ultimately save money. Another example can be found in manufacturing. A factory may produce multiple products using limited resources, such as labor and materials. By applying linear programming (线性规划), the factory can determine the optimal mix of products to manufacture that maximizes profits while adhering to resource constraints. In conclusion, linear programming (线性规划) is a powerful tool that helps decision-makers optimize their operations in various industries. By understanding the components of linear programming (线性规划) and how to apply it effectively, businesses can make informed choices that lead to improved efficiency and profitability. As technology continues to advance, the relevance of linear programming (线性规划) will only grow, making it an essential skill for professionals in many fields.

线性规划是一种用于优化特定结果的数学方法，例如在特定约束条件下最大化利润或最小化成本。这种技术在经济学、工程学、军事操作和运输等多个领域都有广泛应用。线性规划的核心思想是从满足所有给定约束的可行解集中找到最佳解决方案。要更好地理解线性规划，首先需要定义目标函数，它代表我们希望实现的目标。例如，一家公司可能希望根据生产的产品数量来最大化其利润。目标函数通常表示为线性方程。接下来，我们有约束条件，这些是必须满足的限制或要求。这些可以包括资源可用性、生产能力和市场需求。每个约束也可以表示为线性方程或不等式。可行区域，即所有约束重叠的区域，在线性规划中至关重要，因为它包含满足指定条件的所有可能解决方案。图形法是可视化线性规划的一种方式。通过在图上绘制目标函数和约束条件，我们可以识别可行区域并确定最优解决方案。然而，这种方法仅限于两个变量的问题。对于涉及多个变量的更复杂问题，则采用其他技术，如单纯形法或内点法。线性规划的一个实际应用是在运输行业。公司经常面临在满足交货时间表和客户需求的同时最小化运输成本的挑战。通过使用线性规划，他们可以优化运输路线，高效分配资源，最终节省资金。另一个例子可以在制造业中找到。一个工厂可能会使用有限的资源（如劳动力和材料）生产多种产品。通过应用线性规划，工厂可以确定最佳的产品生产组合，以最大化利润，同时遵循资源约束。总之，线性规划是帮助决策者在各个行业优化其运营的强大工具。通过理解线性规划的组成部分以及如何有效应用它，企业可以做出明智的选择，从而提高效率和盈利能力。随着技术的不断进步，线性规划的相关性只会增加，使其成为许多领域专业人士必备的技能。