A linear programming problem is one that is concerned with finding the optimal value (maximum or minimum) of a linear function of several variables .

Traffic signal control types of problems cannot be solved by linear programming methods, because there is no need for optimization in such problems.

In linear programming feasible region (or solution region) for the problem is given by the common region determined by all the constraints including the non – negative constraints x ⩾ 0, y ⩾ 0

In linear programming infeasible solutions fall outside the feasible region . In other words, it the region other than the feasible region is called the infeasible region.

In linear programming, any point in the feasible region which gives that gives the optimal value (maximum or minimum) of the objective function is called optimal solution. In other words, it satisfies all the constraints as well as the objective function .

Let R be the feasible region (convex polygon) for a linear programming problem and let Z = ax + by be the objective function. When Z has an optimal value (maximum or minimum), where the variables x and y are subject to constraints described by linear inequalities then , optimal value must occur at a corner point (vertex) of the feasible region.

Let R be the feasible region for a linear programming problem, and let Z = ax + by be the objective function. If R is bounded, then the objective function Z has both a maximum and a minimum value on R and each of these occur at the corner point (vertex) of R.

Let R be the feasible region for a linear programming problem,and let Z = ax + by be the objective function. If R is bounded, then the objective function Z has both a maximum and a minimum value on R and each of these occurs at a corner point (vertex) of R.

A maximum or a minimum may not exist for a linear programming problem if The feasible region is unbounded .

In Corner point method for solving a linear programming problem the first step is : To find the feasible region of the linear programming problem and determine its corner points (vertices) either by inspection or by solving the two equations of the lines intersecting at that point.