 Hello and welcome to the session. In this session we discuss the isocost method of solving linear programming problems. Isocost method is the method of minimizing the iso profit method. We are given an objective function z equal to a x plus b y, s i and arbitrary chosen fixed value k to this objective function z. This represents some straight line, straight line is called the isocost and for different values of the objective function z we obtain different lines. That is we obtain a family of isocost lines. Let us consider a linear programming problem minus the objective function z equal to 4 x plus 6 y to the constraints given as plus 2 y greater than equal to 18 plus y greater than equal to 75 and the non-negative constraints x greater than equal to 0 and y greater than equal to 0. So our first step involved in the isocost method to solve this problem is to find the feasible region which is written by graphing these constraints. So when we graph all these constraints we would obtain a common region to all these constraints that common region would be the feasible region for this problem. This shaded region is the common region written by the constraints feasible region. As you can see this feasible region is unbounded and we have also found the point of intersection of these two lines as the point f that coordinates 14 and 33. So we have DFE as the feasible region. This feasible region is unbounded. Now in the next step you have the objective function z equal to 4 x plus 6 y assign a convenient value to the objective function z let z be equal to minus 4 x plus 6 y be equal to say 16 which is the common multiple of 4 and 6. We take 4 x plus 6 y equal to 60 or you can say 2 x plus 3 y equal to 30 as equation 1. Now let's graph this equation to get a straight line. So we obtain this line p1 q1 that is p1 q1 represents this equation 1 which is 2 x plus 3 y equal to 30. Now since we have that the objective function is of minimization type so we will draw lines parallel to the line p1 q1 a thing such a line which is nearest to the origin and has at least one point common to the feasible region. So to draw another line parallel to p1 q1 we take let the objective function 4 x plus 6 y be equal to a constant say 120 or this equation could be written as 2 x plus 3 y is equal to 60. Now we will graph this equation and let this equation be equation number 2 change a line p2 q2 we obtain a line p2 q2 parallel to p1 q1 and the line p2 q2 represents equation 2 and p2 q2 is drawn parallel to the line p1 q1. So on drawing lines parallel to p1 q1 we obtain a line p3 q3 parallel to p1 q1 such that it has one point that is the point f the feasible region p2 q3 is a line parallel to p1 q1 is nearest to the origin. It also has a point f with coordinates 14 33 common to the feasible region thus the optimal solution is given by x equal to 14 and y equal to 33 the value z is equal to 10 to 14 plus 6 into 33. That is we substitute x as 14 and y as 33 in the objective function z this is equal to 56 plus 98 which comes out to be equal to 254 that is the optimal value of the objective function z is 254 which is the minimum value in this case. So this is how we solve a linear programming problem using isocost method and isocost method is used to minimize the cost to discuss the advantages of linear programming problems. As we have already seen linear programming finds its application in almost all areas of human life it helps in achieving output maximum profit maximum return and investments in evolving exploitation routes. Next we discuss the limitations of the linear programming problems. Linear programming can only be applied when the given information in terms of linear equations in equations and there are several situations in real life when it is not always possible to express the information in the form of linear equations or linear in equations. So in that case linear programming cannot be applied and the linear programming techniques applicable only when related to a problem can be quantified. The qualitative factors like the human relations, behaviors, credibility etc are now taken into account when linear programming techniques are being applied and sometimes fractional values which are irrelevant. Like for example if we say that one fourth of a car and this information is obviously irrelevant so that is not acceptable. So these are the limitations of linear programming. In this session we have understood the method of isocost of solving linear programming problems and also the advantages and limitations of linear programming.