Answer :

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


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