In a cattle breading firm, it is prescribed that the food ration for one animal must contain 14, 22 and 1 units of nutrients A, B and C respectively. Two different kinds of fodder are available. Each unit of these two contains the following amounts of these three nutrients :
| Nutrient | Fodder 1 | Fodder 2 |
|---|---|---|
| Nutrients A | 2 | 1 |
| Nutrients B | 2 | 3 |
| Nutrients C | 1 | 1 |
The cost of fodder 1 is Rs.3 per unit and that of fodder 2 is Rs.2 per unit. Formulate the L.P.P. to minimize the cost.
Let = units of Fodder 1 and = units of Fodder 2 used per animal. Let = units of Fodder 1, = units of Fodder 2. The non-negativity constraints are since a negative quantity produced has no meaning. The ration must supply at least 14 units of nutrient A, 22 of B and 1 of C; Fodder 1 costs Rs.3/unit and Fodder 2 costs Rs.2/unit, so all three nutrient rows become (minimum-requirement) constraints while the objective (cost) is minimized.
The L.P.P. is — Minimize: subject to .
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