Answer :

The above information can be expressed with the help of the following table:

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

Cost of food X = 5x

Cost of food Y = 8y

Cost of the meal 5x+8y

Now,

⟹ x + 2y ≥ 6

i.e. the minimum requirement of Vitamin A in the foods X and Y is 6units, each of which has 1unit and 2 unit of Vitamin A.

⟹ x + y ≥ 7

i.e. the minimum requirement of Vitamin B in the two foods is 7units, each of which has 1 unit of Vitamin B.

⟹ x + 3y ≥ 11

i.e. the minimum requirement of vitamin C in the two foods is 11units, each of which has 1 unit and 3 units of vitamin C.

⟹ 2x + y ≥ 9

i.e. the minimum requirement of Vitamin D in the foods is 9units, each of which has 2 units and 1 unit of Vitamin D.

Hence, mathematical formulation of the LPP is as follows:

Find ‘x’ and ‘y’ that

Minimises Z = 5x + 8y

Subject to the following constraints:

(i) x + 2y ≥ 6

(ii) x + y ≥ 7

(iii) x + 3y ≥ 11

(iv) 2x + y ≥ 9

(v) x,y ≥ 0 (∵ quantity cant be negative)

The feasible region is unbounded.

The corner points of the feasible region are as follows:

Z is smallest at C(5,2)

Let us consider 5x + 8y ≤ 41.

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

The minimum cost of the diet is ₹41

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