Linear Programming: Characteristics, Theory, Methods and Applications

Linear programming is a mathematical method that is used to determine the best possible outcome or solution from a given set of parameters or list of requirements, which are represented in the form of linear relationships. Characteristics of linear programming include constraints, objective’s function, linearity, finiteness, non- negativity, decision variables and data. The theory of linear programming is known as “The General representation Theorem” which will be clearly understood by taking note of the following definitions: “A hyper plane H in R ̃   is a set of the form {x: px = k} where p is a nonzero vector in R ̃ and k is a scalar.”, “A half space is a collection of points of the form {x: px ≥ k} or {x: px ≤ k}”, “A polyhedral set is the intersection of a finite number of Half spaces. It can be written in the form {x: Ax ≤ b} where A is an m x n matrix (where m and n are integers)” and lastly “Let X ϵ R ̃ where n is an integer. The following are the methods of solving linear programming “the linear programming simplex method and the graphical method”. The applications of linear programming are and not limited to the following “engineering field, manufacturing industrials, energy industry, transportation optimization etc”. The advantages of linear programming are “Linear programming provides insights to the business problem, it helps to solve multi-dimensional problem, it helps to take the best optimal solution. The disadvantages of linear programming are as follows: it takes place only with the variables that are linear, it does not consider change of variables, it cannot solve the nonlinear function and impossible to solve a problem that has more than two variables in the graphical method.