Linear Programming: A statistical tool for business decision. 1

The success of any business is a function of the quality of the decisions the business manager makes time to time. In a complex business environment, decision making is very critical, and the survival of the business is hinged on it.  In making business decisions, business managers, often times, rely on various statistical tools to guide them. One veritable statistical tools in business analysis and decision making is “Linear Programming”. Linear programming, also referred to as linear optimization is a means of achieving the best possible outcome, such as optimization of profit or optimization of production of goods or services at the minimum cost. This is achieved by using mathematical model represented by linear relationships, with the recognition of possible constraints. Linear programming consists of linear functions which are subjected to the constraints in the form of linear equations or in the form of inequalities.

Technically, linear programming is a make-up of two words; ‘linear” and ‘programming”. The earlier defines the relationship between variables with degree one, while the later defines the process of selecting the best solution from various alternatives.  Fundamental to linear programming is the aim of finding optimal solution in business decision making.

Important assumption to consider in the linear programming are:

• Constraints expressed in the quantitative terms
• Relationship between the constraints and the objective function should be linear
• The optimization of the linear function

While its components are:

• Decision Variables
• Constraints
• Data
• Objective Functions

Linear programming problem is characterised by constraint, objective function, and linearity, others are finiteness and decision variable. By application, the constraint is expressed mathematically, regarding resource, the objective function should be specified in quantitative manner, linearity expresses the relationship between two or more variables, finiteness is the finite and infinite factors, non-negativity variable values should be zero of positive, but not negative and decision variables deals with the output, it determines the solution to the problem.

The linear programming is designed to get the optimal solution in dealing with the challenges like; manufacturing problems, diet problems, transportation problems, allocation problems and so on.

The optimal value can be either maximum value or minimum value.

In practical terms of problem solving, linear programming uses different methods to problem solving, however, for the purpose of this article, I shall concentrate to Simplex Methods. The simplex method is one of the most popular methods to solve linear programming problems. It is an iterative process to get the feasible optimal solution. In this method, the value of the basic variable keeps transforming to obtain the maximum value for the objective function.

So,  how does Linear programming practically aid business managers in making decision to either optimize production or maximize profit? This will be dealt with in the next article.