A housewife wishes to mix together two kinds of food, $$X$$ and $$Y$$, in such a way that the mixture contains at least $$10$$ units of vitamin $$A$$, $$12$$ units of vitamin $$B$$ and $$8$$ units of vitamin $$C$$. The vitamin contents of one kg of food is given below :
|Vitamin A||Vitamin B||Vitamin C|
One kg of food $$X$$ costs Rs. $$6$$ and one kg of food $$Y$$ costs Rs. $$10$$. Formulate the above problem as a linear programming problem and find the least cost of the mixture which will produce the diet graphically. What value will you like to attach with this problem ?