What is Linear Programming? What does linear programming mean

It is a mathematical discipline that mainly studies algebraic problems.

Linear programming is an important branch of operations research that has been researched earlier, developed rapidly, widely used and more mature, and it is a mathematical method to assist people in scientific management. In economic activities such as economic management, transportation, industrial and agricultural production, improving economic results is an indispensable requirement of people, and improving economic results generally through two ways: one is technical improvement, such as improving production processes, using new equipment and new raw materials.

The second is the improvement of production organization and planning, that is, the rational arrangement of human and material resources. Linear programming studies the rational arrangement of human and material resources under certain conditions to achieve the best economic effect.

In general, the problem of finding the maximum or minimum value under the constraints of the linear objective function is collectively referred to as the linear programming problem. The solution that satisfies the linear constraint is called the feasible solution, and the set of all the feasible solutions is called the feasible domain. Decision variables, constraints, and objective functions are the three elements of linear programming.

Application: In various management activities of the enterprise, such as planning, production, transportation, technology and other issues, linear programming refers to the selection of the most reasonable calculation method from the combination of various constraints, and the establishment of linear programming model to obtain the best results.

Linear programming. It is a mathematical discipline that mainly studies algebraic problems, and many people don't know about linear programming, so what is linear programming?

1. Linear programming (LP) is operations research.

It is an important branch of early research, rapid development, wide application and mature method, and it is a mathematical method to assist people in scientific management.

2. Blind to study the extreme value of the linear objective function under linear constraints.

Mathematical theories and methods of problems. Abbreviated as LP.

3. Linear programming is an important branch of operations research, which is widely used in military operations, economic analysis, business management, and engineering technology. It provides a scientific basis for making optimal decisions on the rational use of limited human, material, financial and other resources.

Linear programming is a mathematical optimization technique that finds the optimal solution or approximate optimal solution by establishing a mathematical model that describes the linear relationships and constraints of a set of decision variables. In fields such as business, industry, engineering, and science, linear programming is widely used to solve a variety of problems, such as resource allocation, cost minimization, profit maximization, and more.

The basic model of linear planning consists of an objective function and a set of constraints.

The methods for solving linear programming problems include the ** method, the simplex method, the interior point method, etc. Among them, the simplex method is one of the most commonly used methods. In this method, through continuous iteration, the approximate solution of the optimal solution is found until a certain accuracy requirement is met.

In practice, linear programming problems can be very complex and require the use of specialized software and computer programs to solve.

Linear programming has a wide range of applications in a variety of nuclear fields. For example, in production planning and scheduling, linear programming can be used to determine the optimal resource allocation and production flow to minimize costs or maximize production efficiency. In transportation problems, linear programming can be used to solve problems such as vehicle routing, cargo loading, and optimal routes to improve transportation efficiency and reduce costs.

In addition, linear programming can also be used for various problems in the fields of power systems, finance, and military, such as power allocation, portfolio optimization, and equipment allocation.

In conclusion, linear programming is a powerful mathematical tool that can be used to solve a variety of complex optimization problems. By establishing a suitable mathematical model and selecting a suitable solution method, we can find the optimal solution or approximate optimal solution, so as to improve the efficiency and accuracy of decision-making.

Zhuyin one one

Pinyin xiàn xìng guī huà

Basic Definition

A branch of operations research, which uses charts and other demonstration programs to find a scientific method of how to accomplish the most tasks with the least amount of manpower and material resources. Linear programming can solve the problems of reasonable scheduling of vehicles, reasonable allocation of materials, reasonable arrangement of labor, and reasonable allocation of land planting area.

Chinese Dictionary Compendium Linear Programming

A mathematical method to study how to get the maximum benefit with the least expenditure under the constraints of limited human and material resources and the market.

Through careful linear planning, the company's performance this year has doubled compared with last year.

Chinese Dictionary Revised Version Linear Programming 1 1

Mathematical methods are used to study how to obtain the maximum benefits with the least expenditure under the constraints of limited manpower, material resources and the resistant beam market.

Citations and explanations A branch of operations research that uses charts and graphs to demonstrate the scientific method of how to accomplish the most tasks with the least amount of manpower and material resources. Linear programming can solve the problems of reasonable vehicle scheduling, reasonable allocation of materials, reasonable arrangement of labor, and reasonable allocation of land planting area.

Linear programming (LP) is an important branch of mathematical programming in operations research. Since 1947 g b.

Since Dantzig proposed the simplex method for solving linear programming, linear programming has become theoretically mature, and it is one of the basic methods often used in modern management of linear programming because computers can handle thousands of constraints and decision variables in practical practice. When solving practical problems, it is necessary to reduce the problem to a linear programming mathematical model, and the key and difficulty lies in selecting the appropriate decision variables to establish an appropriate model, which directly affects the solution of the problem.

The objective functions and constraints of linear programming problems are linear functions. The constraint is denoted as subject to). The objective function can be the maximum or minimum value, and the inequality sign of the constraint can be less than or greater than the sign.

The (mathematical) standard type of a general linear programming problem is.

An example of linear programming.

Answer: If A produces x 100 kilograms and B produces y 100 kilograms, then the feasible domain is:

30x+15y≤2000

25x+10y≤1500

Objective function: z=3000x+2000y

When x=0 and y=400 3 are obtained from the image, z is maximum, and z=800000 3.

Make the feasible domain yourself (make the straight line when taking the equal sign, and then determine the region--- this can take a special value point, such as the origin, if the conditions are met, then it is the area where the point is located, and vice versa), just find the coordinates of several points of the feasible domain triangle, take the edge where x=1 is located as the base, and the abscissa -1 of the corresponding vertex is high, and the area will come out.

The second question is to look directly at the slope and do the translation. If you really don't know how to look, you can observe whether the slope coincides with the known boundary, if not, just bring three vertices in to see, the largest and the smallest will come out

Hello: luckyihongli is happy to be able to answer the question for you.

Solution: (1) It is surrounded by x>=0, x+3y>=4, 3x+y<=4.

Let y1=-4 3x+4 3, intersect the y-axis at the point m(0,4 3).

Let y2=-3x+4 and the y-axis intersect the point n(0.).，4）

Then y1 and y2 intersect at the point p and get p(

It can be seen that the region represented by x>=0, x+3y>=4, and 3x+y<=4 is PMN

s△pmn=1/2x│mn│x│px│=1/2x8/3x1=4/3

It can be seen that y=kx+4 3 also passes the point m(0,4 3).

Let the intersection of y=kx+4 3 and y2 be h, then hx=8 (3k+9) can be obtained

By the straight line y=kx+4 3 points two parts of the PMN area equal.

i.e. s hmn=1 2s pmn=1 2x4 3=1 2x mn x hx =1 2x8 3x8 (3k+9).

Get k = 7 3

2) The planar area represented by a as the inequality group x<=>=<=2 can be obtained after drawing.

a is the area of an isosceles right-angled triangle with a right-angled side of 2, i.e., a=1 2x2x2=2 (fixed value).

It should be that when k changes continuously from -2 to 1, what is the area of the moving line x+y=k sweeping through that part of the area in a.

Let y-x=2 intersect the x-axis at the point a, then a(-2,0).

Intersects with the y-axis at point b, b(0,2).

Let the straight line y=-x+k

When k=-2, the straight line passes through the point a(-2,0).

When k=1, the y-axis of the line intersection is the point c(0,1), which intersects the line ab at the point d (dx can also be found).

The swept area is quadrilateral: saocd=a-s, cdb=2-1, 2x1x1, 2=7, 4

The CDB is an isosceles right triangle with hypotenuse BC = 1).