Introduction of Linear Programming (LP)
To understand LP , first we need to understand mathematical programming thoroughly. So what is mathematical programming (MP).
MP is the branch of management science that deals with solving optimization problem, in which we want to maximize function (such as profit, expected return or efficiency) or minimize the function( such as cost. time or distance), Usually in a constrained environment. The recommended course of action is known as program : hence, the term MP is used to describe such problems.
MP consist of 3 components (Elaborate 3 function) 1. Decision variable: - Which is controlled or determined by the decision maker 2. Objective Function:- Its to be maximize or minimize 3. Constraints:- Restrictive set of conditions that must be satisfied by any solution to the model.
The most widely used mathematical model are LP models.
LP models
A LP model is model that seeks to maximize or minimize a linear objective functions subject to a set of linear constraints.
Large company such as the San Miguel corporation, Texaco, American airlines and general motors have used linear models to affect efficiency and improve the bottom line . But LP can also be applied in smaller venues. In fact a wide variety of cases lend themselves to linear modeling , including problems from such diverse areas such as manufacturing, marketing, investing , advertising, trucking, shipping, agriculture, nutrition, E-commerce, restaurant and travel industry.

Importance LP 1. Many problem naturally lend themselves to LP formulation, and many other problems can be closely approximated by models with this structure 2. Efficient solution techniques exist for solving models of this type 3. The output generated from lp packages provide useful “what – if “ information concerning the sensitivity of the optimal solution to