constraints The main important feature of linear programming model is the presence of linearity in the problem. The use of linear programming model arises in a wide variety of applications. Some model may not be strictly linear, but can be made linear by applying appropriate mathematical transformations Still some applications are not at all linear, but can be effectively approximuted by linear models. The ease with which linear programming models can usully be solved makes an attractive means of dealing with otherwise intractable nonlinear models. 2.2 Linear Programming Problem Formulation The linear programming problem formulation is illustrated through a product mix problem. The product mix problem occurs in an industry where it is possible to manufacture a variety of products. A product has a certain mirgin of profit per unit, and uses a common pool of limited resources. In this case the lineat programming technique identifies the products combination which will maximize the prodit subject to the availability of limited resource constraints. Example 2.1: Suppose an industry is manufacturing tow types of products Pl and P2. The protits per Kg of the two products are Rs 30 and Rs.40 respectively. These two products require processing in three types of machines. The following table shows the available machine bours per day and the time required to each k10 18 MA2000 Olive Tapas i Man machine to produce une Ks of Pland 12. Formulate the problem in the form of linear programming model Prolake PO RM Machine Machine Machine P2 R. 40 2 5 6 Total available Machine hurday KO NO 1100