Reshma wishes to mix two types of food `P` and `Q` in such a way that the vitamin contents of the mixture contain at leat 8 units of vitamin A and 11 units of vitamin B. Food `P` cost 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.

Explanation

Let `x` kg of first type of food and `y` kg of second type of food be mixed.

According to the problem,
Minimise `Z=60x+80y`
and constraints `xge0, yge0`
`3x+4yge8,5x+2yge11`
First, draw the graph of the lines `3x+4y=8` and `5x+2y=11`

Now find the feasible region from the constraints `3x+4yge8,5x+2yge11,xge0,yge0` and shade it. The vertices of this shaded region are `A(0,11/2),B(2,1/2)` and `C(8/3,0)`. We find the value of `Z` at these vertices.

Therefore, the minimum cost of the mixture is Rs. 160.