A housewife wishes to mix together two kinds of food, and , in such a way that the mixture contains at least 10 units of vitamin units of vitamin and 8 units of vitamin The vitamin contents of of each food are given below.

If of food cost and of food costs , find the minimum cost of the mixture which will produce the diet.

Solution:

Let and be number of kilograms of food and .
According to the question,

Minimize
The feasible region determined is given by

The feasible region is unbounded. The corner points of feasible region are , . The value of at corner points are

The minimum value of is 52 at point .
Hence, the diet should contain 2 kgs of food and 4 kgs of food for the least cost of Rs. 52 .