A diet is to contain at least 80 units of vitamin A and 100 units of minerals. Two foods F₁ and F₂ are available. Food F₁ costs Rs 4 per unit food and F₂ costs Rs 6 per unit. One unit of food F₂ contains 3 units of vitamin A and 4 units of minerals. One unit of food F₂ contains 6 units of vitamin A and 3 units of minerals. Formulate this as a linear programming problem. Find the minimum cost for diet that consists of mixture of these two foods and also meets the minimal nutritional requirements.

Let the diet contain x units of food F₁ and y units of food F₂.
Let Z be the cost.
Table

We are to minimise
Z = 4x + 6y
subject to constraints
3x + 6y ≥ 80
4x + 3y ≥ 100
x ≥ 0, y ≥ 0
              Now we draw the graph of 3x + 6y = 80
          For x = 0,   6 y = 80  or   y = 
           For y = 0,   3 x = 80   or   
     
Again we draw the graph of 4x + 3 y = 100
For x = 0,  3y = 100   or   y = 
For y = 0,   4x = 100  or  x = 25
   line meets OX in B(25, 0) and OY in M        

Since feasible region satisfies all the constraints.
∴ shaded region is the feasible region which is unbounded and has comer points are 

Since feasible region is unbounded.
∴ we are to check whether this value is minimum.
For this we draw the graph of
4x + 6y < 104    ...(1)
Since (1) has no common point with feasible region.