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Linear programming is a mathematical method of allocating limited resources to achieve a goal such as maximizing profits and minimizing costs.

Linear programming problems are widely applied in the economic, industrial, military, social and others. Linear programming deals with the explanation of a case in the real world as a mathematical model consisting of a linear objective function with multiple linear constraints.

Linear programming has several properties or characteristics. Linearity properties of a case can be determined by using graphs (scatter diagram) or use a hypothesis test. Met if the proportional nature of the contribution of each variable in the objective function or limit the use of resources proportional to the level of the variable value.

Additivitas nature assumes that there is no cross-product terms between the various activities. Divisibilitas nature of the activity means the unit can be divided into any fractional levels. The nature of certainty demonstrated that all parameters of the model in the form of constants. This means that the objective function coefficients and the limiting function is a definite value, not the value of the specific opportunities.

Linear program is a field of science that is learned in mathematics courses. The linear programming problems with studying the relationships between all the variables that are linear. In linear programming, a lot of dealing with constraints, functions, responsibilities visible and invisible replied.

Linear Programming method first discovered by U.S. statisticians named Professor. George Dantzig (Father of the Linear Programming). Linear programming is a mathematical method of allocating limited resources to achieve a goal such as maximizing profits and minimizing costs. Linear programming problems are widely applied in the economic, industrial, military, social, and others. Linear programming deals with the explanation of a case in the real world as a mathematical model consisting of a linear objective function with multiple linear constraints.

In completion of the Linear programming optimization, there are several steps that must be carried out, namely:

• Determine the decision of variables.
• Making objective function.
• Formulate constraints.
• Describing in graphic form.
• Determine the area of possibility / "feasible".
• Determining the optimum solution.

There are two types of approaches are commonly used in the Linear Programming methods, namely:

Graph Method

• Used to complete the optimization with a maximum of 2 variables.
• For more than two variables, the solution using the second method.

Simplex Method

• Used to process the number of variables is more than 2.
• Stages in simpeks method is more kompeks than the graphical method.

There are three stages in the use of linear programming techniques. First, the problem must be identified as something that can be solved by linear programming. Second, the problem of unstructured money should be formulated in a mathematical model to become structured. Third, the model must be solved by mathematical techniques that have been made.

Linear programming techniques illustrate that the relationship linear functions in the solution of mathematical models that have been set in steps of mathematics called program. Thus, linear programming is a model consisting of linear relationships that describe the company's decision with a goal and resource constraints. Therefore, the linear programming model consists of decision variables, objective function and the constraints.

Linear Programming Method

North West Corner Method

North West Corner is one method of searching for feasible solutions early base equilibrium transport problem.

Least Cost Method

Same with the North West Corner method, Least Cost method is one method of searching for feasible solutions early base equilibrium transport problem.

Vogel Approximation Method

Same with the North West Corner method, Vogel's approximation method is one method of searching for feasible solutions early base equilibrium transport problem.

Methods Stepping Stone / Stone Springboard

Methods Stepping Stone / Stone Springboard is one method of testing the optimality of a transport problem.

MODI method (Modified Distribution)

Same with the Stepping Stone method, MODI method is one method of testing the optimality of a transport problem. MODI method is mrupakan metod development of Stepping Stone.

Methods Karmakar

Karmakar method is one method to solve linear programming problems.

Quadratic Interior Point Methods Exstended (EQIP)

Same with the method of Karmakar, EQIP method is one method to solve linear programming problems. EQIP is a deterministic method which is a method of Karmakar method development. EQIP method is developed by James A. Momoh. EQIP method can be used to solve quadratic programming problems (non-linear).

Simplex Method

Simplex method is one method to solve linear programming problems with constraints. This method is a powerful method to solve two variable linear programming problems, for more details simplex method can see in this video link. This method is very slow, but as the development of the times, the simplex method can be solved by software management operations such as TORA, LINDO, LINGO, and others. Simplex method is an iterative method is stopped if the terms have been met.

Dual-Simplex Method

Similarly, the Simplex method, Dual-Simplex method is one method to solve linear programming problems with constraints. Dual-Simplex method moves from a less optimal feasible solution becomes more feasible optimum solution.

Big-M method

Similarly, the Simplex method, Big-M method is one method to solve linear programming problems with constraints. Big-M method is used to solve the constraint functions inequality diverse types.

Dual-phase method

Similarly, the Simplex method, Dual-Phase method is one method to solve linear programming problems with constraints. Dual-phase method is used to solve the constraint functions inequality diverse types, there is even an equation.

Graph Method

As we learned in high school, linear programming problems can be solved by a graphical method

Bisection / biseksi

Bisection / biseksi is one method to solve linear programming problems without constraint functions.

Golden section

Golden section is one method to solve linear programming problems without constraint functions.

Steepest descent

Steepest descent is one method to solve linear programming problems without constraint functions.

Davidon Fletcher

Davidon Fletcher is one method to solve linear programming problems without constraint functions.

Linear Programming Function

Linear programming can be applied to various fields of study. This method is most widely used in business and economics. Also, it can also be utilized in a number of engineering calculations. For example, in economics, the objective function can be associated with an optimal arrangement of resources to obtain the maximum profit or minimum cost, while the limit function illustrates the limits of available capacity optimally allocated to various activities. Industries that utilize linear programming among the transportation industry, energy, telecommunications, and manufacturing. Linear programming is also shown to be beneficial in making models of various types of problems in planning, designing routes, scheduling, assignments, and design.

That's a little explanation of Linear Programming. Hopefully useful explanation given to you.