Linear programming is a mathematical method for optimizing operations given restrictions. In a business, the businessman is interested to get maximum profit, minimum investment, and maximum production by using limited resources. This type of problem can be solved by a technique known as linear programming.

The following are some of the terms used in linear programming:

a)      Objective function: A linear function whose maximum or minimum values or both values are to be calculated is called objective function.

For example, let x and y be the number of two types items A and B produced from a factory respectively. On selling A and B items there are profits of Rs. 10 and Rs. 20 per unit. Then the profit function is P=10x+12y, which is to be maximized. Then the profit function is the objective function.

b)     Constraints: The conditions or restrictions in solving a linear programming problem which is to be satisfied by the variables of the objective function. In linear programming problems, the inequalities are taken as constraints. For example, x+y>=1000 etc.

c)      Feasible region: A closed plain region bounded by the intersection of finite number of boundary lines is called feasible region (or convex polygonal region). It is the common solution region bounded by given constraints

d)     Feasible solution: The values of variables used in the objective function which satisfy all the given conditions are called feasible solution.

Therefore, Linear programming is a mathematical technique of getting a maximum or minimum or both maximum and minimum values of an objective function satisfying given constraints.

Standard maximization problem

Linear programming is said to be a standard maximization problem if we are to find the maximum value of the objective function

All the decision variables x and y are constrained to be non–negative

Standard minimization problem

Linear programming is said to be a standard minimization problem if we are to find the minimum value of the objective function

All the decision variables x and y are constrained to be non–negative

Steps to find the optimal value of the objective function

i. Change linear programming problem to mathematical form if necessary

ii. Express the inequalities into their corresponding equations

iii. Get the feasible region from the graph and the obtain vertices of the feasible region.

iv. Calculate the value of the objective function at different vertices

v . find the vertex of the objective function at optimal value.

vi. Interpret the optimal value