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INTRODUCTION

(a) Linear Programming (LP) is a mathematical technique, which is used for allocating limited resources to a number of demands in an optimal manner. When a set of alternatives is available and one wants to select the best, this technique is very helpful. Management wants to make the best use of organizational resources. Human resources, which may be skilled, semi-skilled or unskilled must be putto optimal use. Similarly, the material resources like machines must be used in an effective manner. Time is very important resource and any job must be completed in allotted time. Application of LP requires that the following conditions must be met:

(b) There must be a well-defined objective of the organization such as:

  1. Maximizing profit
  2. Minimizing cost

This objective function must be expressed as a linear function of variables involved in decision-making.

(c) There must be a constraint on availability of resources for the objective functions i.e. for achieving maximum profit or for reducing the cost to minimum.

LP technique establishes a linear relationship between two or more variables involved in management decisions described above. Linear means it is directly proportional i.e. if 5 percent increase in manpower results in 5 percent increase in output it is a linear relationship.

(d)Alternative course of action must be available to select the best, for example if a company is producing four different types of products and wants to cut down one product, which one should it stop manufacturing. The problem gives rise to a number of alternatives and so LP can be used.

(e) Objeciive function must be expressed mathematically i.e. we must be able to develop a linear mathematical relationship between the objective and its limitation. Linear equations are of first degree i.e. if we want x andy as the variable, the equation 5x + 10y = 20 is a linear equation in which x and y can assume different values. However, an equation like 5x2+ 10y2= 200 is not a linear equation, because of the variable x and yare squared, this is a typical second degree equation.