Q. 25.0( 3 Votes )

A diet for a sick

Answer :

The above information can be expressed in the form of the following table:



Let the quantity of the foods be ‘x’ and ‘y’ respectively.


Cost of food A = 4x


Cost of food B = 3y


Total cost of the combination = 4x + 3y


Now,


200x + 100y ≥ 4000


i.e. the minimum requirement of vitamins from the two foods should be 4000.


x + 2y ≥ 50


i.e. the minimum requirement of minerals from the two foods should be 50.


40x + 40y ≥ 1400


i.e. the minimum requirement of calories from the two foods should be 1400


Hence, mathematical formulation of LPP is as follows:


Find ‘x’ and ‘y’ which


Minimize Z = 4x + 3y


Subject to the following constraints:


(i) 200x + 100y ≥ 4000


i.e. 2x + y ≥ 40


(ii) x + 2y ≥ 50


(iii) 40x + 40y ≥ 1400


i.e. x + y ≥ 35


(iv) x,y ≥ 0 ( quantity cant be negative)



The feasible region is unbounded.


The corner points of the feasible region is as follows:



Z is smallest at B(5,30)


Let us consider 4x + 3y ≤ 110


As it has no intersection with the feasible region, the smallest value is the minimum value.


The minimum cost of foods is ₹110


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