**Linear Programming **

*(Key Points)*

① Linear Programming Problems – Problems which concern with finding the minimum or maximum value of a linear function Z (called objective function) of several variables (say x and y), subject to certain conditions that the variables are non-negative and satisfy a set of linear inequalities (called linear constraints) are known as linear programming problems.

② Objective function – A linear function

*z = ax + by*, where a and b are constants, which has to be maximised or minimised according to a set of given conditions, is called a linear objective function.

③ Decision Variables – In the objective function

*z = ax + by*, the variables x, y are said to be decision variables.

④ Constraints – The restrictions in the form of inequalities on the variables of a linear programming problem are called constraints. The condition x ≥ 0, y ≥ 0 are known as non – negative restrictions.