question_answer 11)

Reshma wishes to mix two types of food P and Q in such a way that the vitamin contents of the mixure contain at least 8 units of vitamin A and 11 units of vitamin B. Food costs Rs.6/kg. and food Q costs Rs.80/kg. Food P contains 3 units/kg of vitamin A and 5 unit/kg. Of vitamin B while food Q contains 4 units/kg of vitamin A and 2 units/kg of B. Determine the minimum cost of the mixture.  

Answer:

Let number of units of food type P = x       and number of units of food type Q = y             The contents of food are given below :             Therefore the above L.P.P. is given as       Minimize, C = 60x + 80y, subject to the containts       3x + 4y  8; 5x + 2y  11, x, y  0       L1 : 3x + 4y = 8        L2 : 5x + 2y = 11                              Here cost C is minimum at  and  and is Rs.160.       Since the region is unbounded, therefore, 160 may or may not be the minimum value of C. For this draw graph of inequality 60x + 80y < 160.       i.e. 3x + 4y < 8       L : 3x + 4y = 8             Clearly open half plane has no common points with the feasible region, so minimum value of C is 160.