where X1, X2, x3 = 0, since negative production has no meaning and is not feasible. Step 4: Mention the objective quantitatively and express it as a linear function of variables. In the present situation, objective is to maximize the profit. i.e., maximize Z = 4x; + 3x2 + 6xz. Step 5: Put into words the influencing factors or constraints. These occur generally because of constraints on availability (resources) or requirements (demands). Express these constraints also as linear equations/inequalities in terms of variables. Here, constraints are on the machine capacities and can be mathematically expressed as 2x, + 3x2 + 2x3 = 440, 4x, + 0x2 + 3x3 s 470, 2x + 5x2 + Oxz S 430. Therefore, the complete mathematical (L.P.) model for the problem can be written as maximize Z = 4x, + 3x2 + 6x3, subject to constraints, 2x + 3x2 + 2xz S 440, 4x + 3x3 s 470, 2x + 5x2 3 430, where x1, x2, X3 20. f1 EXAMPLE 2.6-2 (Diet Problem) A person wants to decide the constituents of a diet which will fulfil his daily requirements of proteins, fats and carbohydrates at the minimum cost. The choice is to be made from four different types of foods. The yields per unit of these foods are given in table 2.2. TABLE 2.2 Food type Cost per unit 45 40 Yield per unit Proteins Fats Carbohydrates 1 3 2 6 2 4 2 4 3 8 7 7 4 6 5 4 Minimum requirement 800 200 700 Formulate linear programming model for the problem. 85 65