Reshma wishes to mix two types of food P and Q in such a way that the vitamin contents of the mixture contain at least 8 units of vitamin A and 11 units of vitamin B. Food P costs Rs 60/kg and Food Q costs Rs 80/kg. Food P contains 3 units/kg of Vitamin A and 5 units / kg of Vitamin B while food Q contains 4 units/kg of Vitamin A and 2 units/kg of vitamin B. Determine the minimum cost of the mixture.
Let the mixture consists of x kg of food P and y kg of food Q. ∴ x ≥ 0 and y ≥ 0
According to given situation in the question, the information can be tabulated as follows:
The mixture must contain at least 8 units of vitamin A and 11 units of vitamin B.
∴ The constraints are:
3x + 4y ≥ 8 and
5x + 2y ≥ 11.
Where x ≥ 0 and y ≥ 0
Total cost of ‘Z’ of purchasing food is Z= 6ox+ 80y
The mathematical formulation of the given problem is: minimize Z= 6ox + 80y…….1
Subject to constraints
3x + 4y ≥ 8 and
5x + 2y ≥ 11.
Where x , y ≥ 0
The graphical representation shows the feasible region is unbounded.
The corner points of the feasible region are 
The values of Z at these corner points are
As the feasible region is unbounded
∴ 160 may or may not be the minimum value of Z
But it can be seen that the feasible region has no common oint with 3x+4y <8
So the minimum cost of the mixture will be Rs160 at the line segment joining the points 