 Myself Satish Thalange, Assistant Professor, Department of Civil Engineering, Wolchen Institute of Technology, Solapu. In today's session we are going to see regarding the formulation of the problem in the linear programming problem. In that we are going to see one of the case that is of a maximized case. Now at the end of the session, the particular learner will be able to convert the real word problem into the form of the mathematical equation that is the linear programming problem. See what is the linear programming problem? The linear programming problem is nothing else, it is one of the mathematical modeling technique which involves the objective functions, decision variables and the set of constraints. After the decision variables which are involved, they are restricted with the non-negative sign. The objective of the linear programming problem is to have always to try to maximize the profit or you can say to maximize the benefit or production of the particular product so that it should have the benefit to the company and also its objective is to minimize the time requirement for the manufacturing or to minimize the loss or the wastage of the resource. So once we come to know what is our objective to learn the linear programming problem, it is very helpful to make a decision. Now before solving or getting the solution for the particular problem, it is a most important necessary thing is to formulate the real word example in the mathematical form. That is nothing else, the formulation of the particular problem in which we convert the real word problem into the mathematical equations which is known as the linear programming problems. Here we are converting the problem in the linear programming problem. And we are going to use some of the techniques to get the solution which I mean mentioned the graphical method, simplex method, big M method and two phase method. But in today's session we are just going to focus on the formulation of the particular problem. In the successive sessions we can observe the graphical methods and the many more techniques which are involved for solving of the linear programming problem. Now the step one, we have to observe, study and understand the real word problem. After knowing all this we should be able to identify the correct problem and we have to describe the objective of the particular problem that is known as the objective function. Next comes regarding the decision variables present in the problem. This are the particular terms which are helpful to define the particular problem in the quantitative manners. And after finalizing the decision variables we have to assign the restrictions to them in the accordance to the sign. So always the variables are called as the non-negative variables. And after finalizing the decision variables we have to define the objective function equation by using the decision variables. So write the objective function using the decision variables. This objective function may be maximized case or minimized case. And next steps come regarding identifying the constraints and write the set of constraints which are involved in the particular decision variables. This constraints may be equality equations or inequality equations. And finally we have to give the restrictions to the decision variables with the sign. So now let's see one of the example. In the present question we are observing that the company is of the manufacturing type and its manufacture the table and chair. And the raw material available or you can say used is wool and the labour time which is been defined in the hours. And they have defined the unit profit of the table as well as unit profit of the chair also. Now let's start to format the problem. And the table which is giving you the overall picture of what quantity of requirement of the wood for the chair and the table is been mentioned and the labour hours required for the manufacturing of table and chair has been mentioned in the particular table. So the first step is to identify or you can say observe, study and understand the real world problem. We have observed that it's a particular manufacturing company and its manufacture the table and chair and we have studied that they are interested to find out the particular quantity or you can say to know the appropriate utilizations of resource to maximize the profit. So after identifying the problem we have objectives to define the objective function. In the present case the company management objectives to maximize the unit profit. So the particular table and chair manufacturing issue being such a quantity that the particular company should have maximum profit with the optimum utilization of the raw material as well as their labour time. Now moving towards the step three define the decision variables. As we are observing that the chair and the table are the two products so here we come to know the clear picture that we have to take the two variable particular variable x1 for the table and x2 for the chair. And these two variables x1 and x2 are the non-negative variables. And moving towards the step four we have to write the objective function. As we have seen that in the step two the objective is to maximize the unit profit. So I have written here the maximize case and the z is equal to 60x1 plus 80x2. How this particular objective function equation has been derived you have just seen. The particular they are defining that the unit profit by the table is 60 rupees and from the chair it is 80 rupees. We have defined x1 is of the table and x2 is of a chair. The equation is z is equal to 60x1 plus 80x2. Here we are interested to find out the z value also. So means what profit we are getting based upon the quantity of the table and the chair that is the most important. Means here in the present case we are interested to know also the particular quantity of the or we can say value of the variable that is x1 as well as x2. And as I said we are saying these are these two variables x1 and x2 are non-negative. That means see the particular manufacturing of the table either it will be equal to zero or it will be more than zero not be negative. So the table and chair they have restriction of the particular sign that is fine. Next come the step 5 identify the constraints. As we know this is an example in which there are two constraints wood and the labour. Maximum wood available in the board feet is 300 and the labour hours available in the hours is 110. And this is the values or we can say outcomes which are these cells are representing the 30 is the board square feet required for the table and the 20 is the board feet required for the manufacturing of the chair. And the 5 hours is the table hours or we can say time required for the manufacturing of the table and the 10 is the time requirement for the manufacturing of the chair. Now coming to the point now we have to define the set of constraints there are two constraints as I said first one is of the available of raw material that is wood constraint second is of a labour hours or we can say labour time hours. So 30 x1 plus 20 x2 is less than or equal to 300 because the maximum board feet available with us is 300 and the time hour available with us is 50 x1 plus 10 x2 is less than or equal to 110 labour hour available is 110 hours. So these are the two constraints or set of constraints and finally we have to give the restriction to the particular two variables that's why x1 comma x2 is greater than or equal to 0. This is overall final particular formulated problem the objective function maximize k z is equal to 60 x1 plus 80 x2 and subjected to the constraints 30 x1 plus 20 x2 less than or equal to 30 and 5 x1 plus 10 x2 less than or equal to 110 and x1 comma x2 is greater than or equal to 0. Now let us take a simple example just go through this example and identify the objective function and the number of variables take a pause and read it properly and define the answer hope so this is a answer which you are getting the objective function of the particular example is to maximize the profit and the particular number of decision variables involved are two that is two decision variables for product A and product B. These are the references for today's session thank you.