Q. 64.8( 4 Votes )

A diet is to cont

Answer :

The above information can be expressed in the following table:



Let the quantity of the foods F1 and F2 be ‘x’ and ‘y’ respectively.


Cost of food F1 = 4x


Cost of food F2 = 6y


Cost of Diet = 4x + 6y


Now,


3x + 6y ≥ 80


i.e. the minimum requirement of Vitamins from the two foods is 80units, each of which contains 3units and 6units of Vitamins.


4x + 3y ≥ 100


i.e. the minimum requirement of minerals firm the two foods is 100units, each of which contains 4unit and 3 units of vitamins.


Hence, mathematical formulation of the LPP is as follows:


Find ‘x’ and ‘y’ that:


Minimise Z = 4x + 6y


Subject to the following constraints:


(i) 3x + 6y ≥ 80


(ii) 4x + 3y ≥ 100


(iii) 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


Let us consider 4x + 6y ≤ 104


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


The minimum cost of diet is ₹104.


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