question_answer 23)

A farmer mixes two brands P, and Q of cattle feed. Brand P, costing Rs.250 per bag, contains 3 unitso f nutritional element A, 2.5unitso f element B and 2 units of element C whereas brand Q costing Rs.200 per bag contains 1.5 units of nutritional element A, 11.25 units of element B, and 3 units of element C. The minimum requirements of nutrients A, B and C are 18 units,45 units and 24 units respectively. Determine the number of bags of each brand which should be mixed in order to produce a mixture having a minimum cost per bag ? What is the minimum cost of the mixture per bag ? 

Answer:

Let x and y be the number of bags of brand P and Q of cattle feed.       The contents of each brand are given above : Nutritional         The above L.P.P. is given as       Minimize, C = 250x + 200y, subject to the constraints 3x + 1.5y 2x + 3y .       L1 : 3x + 1.5 y = 18              L2 : 2.5x + 11.25 y = 45       Here the cost is minimum at G(3, 6)       Since the region is unbounded therefore Rs.1950 may or may not be the minimum value of C. For this draw graph of inequality 250x + 200y < 1950.             5x + 4y < 39        L : 5x + 4y = 39                   Clearly open half plane has no common point with the feasible region so minimum value of C is Rs.1950.       For this 3 bags of brand P and 6 bags of brand Q to be mixed to get minimum cost.