 Hello and welcome to the session. In this session we discuss the concept of linear programming problem. First let's discuss what is linear programming. Linear programming is the method used in decision making in business the maximum minimum value of a linear expression linear equations. We have a linear expression subject to satisfy certain given linear equations and we have to find the maximum or minimum value of this linear expression and we would use the linear programming to do this. Now in the word linear programming linear implies that all the mathematical relations that are used in the problem are linear relations and this programming word refers to the method of determining a particular program and you can say the plan of action. This linear expression of these linear equations are known as the linear constraints. The basic terminologies used in linear programming problems as term is linear constraints. We have already discussed that the linear equations are the linear constraints. The limited resources like money, labor, time, materials etc available in the business or industry are to be best utilized and the limitations, the resources, linear equations, the objective function we know that the linear expression for which we have to find the maximum or the minimum value is the objective function and function for invariant variables which is to be maximized or minimized by given linear objective function. A function given by z equal to say ax plus by the function where these a and b are the constants and these variables x and y the decision variables function is to be maximized or minimized is the optimal value of the function the maximum minimum value of an objective function is known as the minimum value. Now for an objective function we either obtain a maximum value or a minimum value and that maximum or minimum value is its optimal value. Next term is feasible solution it is the set of values of the variables the final the optimal solution the solution is the feasible solution which leads to the optimal value and objective function obtain the feasible solution we find out that feasible solution which leads to the optimal value of the objective function and that is called the optimal solution. Now next we have the optimization problem inequalities to discuss the linear programming problem. Now these linear programming problems are a special type of problems and a general linear programming problem objective function can be given constraints. The problem is concerned with finding the low value which is the linear function several variables which are the decision variables the conditions that the variables are negative that of linear inequalities called the linear constraint. In a programming problem we are given an objective function of several variables which are called the decision variables and this objective function is subjected to constraints and also it's given that the variables that is the decision variables are non-negative. This problem we have to find the optimal value of the objective function. Now let's discuss different types of linear programming problems. Now we'll discuss three important linear programming problems the first one is manufacturing problems in these we get a number of units that should be produced each product requires six non-par materials. By problems we determine the amount of kinds of constituents be included minimizing subject to the availability of food their prices. Next type of linear programming problem is the decision problems in this we determine a transportation schedule the cheapest way of transporting factories situated at different locations markets. The main problems or you can say the linear programming problems that we discuss we have the manufacturing problems the bike problems and the transportation problems. It's the fashion that we have understood the topic of linear programming problems.