Page 1 - LESSON NOTES

XII - CHAPTER-12
LINEAR PROGRAMMING PROBLEM

KEY NOTES:

Definitions Related with Linear Programming Problem:

Objective Function: A function, which is to be maximize or minimize subject to given
conditions is called the objective function.

Constraints: The conditions on the variables of an objective function which are in the form of
equations (=) or in – equation (≤, ≥, <, >), called constraints.

Optimal Value: The maximum or minimum value of the objective function is called the
optimal value.

Feasible Solution: Every point of the feasible region of a linear programming problem
which satisfies all constraints is called a Feasible Solution.

GRAPHICAL METHOD FOR SOLVING LINEAR PROGRAMMING PROBLEM (LPP)

The graphical method for solving LPP containing two variables only.

Step – 1 Convert each constraints into equal sign.

Step -2 Find the intercept form of straight line.

Step – 3 find the direction.

Step – 4 find the feasible region of LPP.

Step -5 Find the corner points (vertex point).

Step -6 Tests the vertex point at the objective function. Find the Max. Or Min. value.

Example: 1

Maximize Z = 3x + 4y
Subject to the constraints:
x + y ≤ 4, x ≥ 0, y ≥ 0
Solution:
The feasible region determined by the constraints x + y ≤ 4, x ≥ 0, y ≥ 0 is as follows: