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 contain x kg. of food P and y kg. of food Q.
Clearly x ≥ 0, y ≥ 0.
Let Z be the total cost.
Table

Mathematical formulation of the given problem is as follows:
Minimise Z = 60 x + 80 y
subject to the constraints
3x + 4y ≥ 8
5x + 2y ≥ 11
x ≥ 0, y ≥ 0.
Consider a set of rectangular cartesian axes OXY in the plane.
It is clear that any point which satisfies x ≥ 0, y ≥ 0 lies in the first quadrant.
Now we draw the graph of 3x + 4y = 8
For x = 0,   4y = 8   or  y = 2
For y = 0,  3x = 8   or 

and OY in L(0, 2)
              Again we draw the graph of 5x + 2y = 11
              For x = 0,  2y = 11   or   
              For y = 0,   5x = 11   or  


and OY in      

Since feasible region satisfies all the constraints.
∴ shaded region is the feasible region and it is unbounded.
The corner points are 
  

Since feasible region is unbounded.
∴ we are to check whether this value is minimum.
For this we draw the graph 60x + 80 y < 160 i.e. 3x + 4y < 8    ...(1)
 Since (1) has no common point with feasible region.
         minimum cost  = 160 at  i.e. at points lying on segment joining