question_answer 1)

A diet is to contain at lest 80 units of vitamins A and 100 units of minerals. Two food F1 and F2 are available. Food F1 costs Rs.4 per unit food and F2 costs Rs.6 per unit. A unit of food F1 contains at least 3 units of vitamin A and 4 units of minerals. A unit of food F2 contains at least 6 units of vitamin A and 3 units of minerals Formulate this as a linear programming problem. Find the minimum cost for diet that consists of mixture of these two foods and also meets and minimal nutritional requirements. 

Answer:

Let number of units of food F1­ = x       and number of units of food F2 = y       The contents of one unit of each food is given as :         Therefore, the above L.P.P. is given as       Minimize, C = 4x + 6y, subject to constraints       3x + 6y  4x + 3y       L1 : 3x + 6y = 80      L2 : 4x + 3y = 100                              Here cost is minimum at point E        Minimum cost = Rs.104       Since the region is unbounded therefore Rs.104 may or may not be the minimum value of C. For this draw graph of inequality 4x + 6y < 104.       i.e., 2x + 3y < 52       L : 2x + 3y = 52             Clearly open half plane has no common point with the feasible region so that minimum value of C is Rs.104.