# Introduction to Linear Programming

• ### Introduction to Linear Programming

Due to the increasing complexity of business organizations, the role of the management executive as a decision maker is becoming more and more difficult. During the last thirty years or so several statistical and mathematical techniques have been developed in order to meet this situation. It may be observed that certain problems facing the business […]

• ### Inequality and Compound Inequality

Inequality: An inequality expresses the relative order of two mathematical expressions. The symbols (less than), (less than or equal to), (greater than), (greater than or equal to) are used to write inequalities. Note: The sign of an inequality is unchanged if it is multiplied or divided by a positive number, For example, Similarly, Note: The […]

• ### Examples of Inequality and Compound Inequality

Example: Solve and graph the solution of the inequality Solution: We have Thus, the solution set is Solution Set The graph of the solution set. Example: Solve and graph the solution of the inequality . Solution: We have Here equality is not possible, because 13 is always greater than 12, in . So, the solution […]

• ### Linear Inequalities in Two Variables

The inequalities of the form , , , where , , c are constants, are called the linear inequalities in two variable. The points which satisfy the linear inequality in two variable ‘x’ and ‘y’ from its solution. Graphing the Solution Region of Linear Inequality in Two Variables: Example: Graph the solution set of the […]

• ### Examples of Linear Inequalities in Two Variables

Example: Graph the solution set of the system of linear inequalities Solution: We have The corresponding equations of inequalities (A) and (B) For x – intercept For x – intercept Put in (1) we get Put in (2) we get For y – intercept For y – intercept Put in (1) we get Put in […]

• ### Graphing the Solution Region of System of Linear Inequalities

Example: Graph the solution set of the system of linear inequalities. Solution: We have The corresponding equations of inequalities (A), (B) and (C), we get For x–Intercepts: Put in Eq (1), Eq (2) and Eq (3) we get For y–Intercepts: Put in Eq (1), Eq (2) and Eq (3) we get Test: Put origin as […]

• ### Feasible Solution Set

Corner Point OR Vertex: A point of a solution region where two of its boundary lines intersect is called a corner point or vertex of the solution region. Problem Constraint: In a certain problem from everyday life each linear inequality concerning the problem is called the problem constraint. Non – Negative Constraint OR Decision Variables: […]