Answer :

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

Let the quantity of X and Y purchased be ‘x’ and ‘y’ kgs

Cost of X = 16x

Cost of Y = 20y

Cost of the mixture = 16x + 20y

Now,

⟹ x + 2y ≥ 10

i.e. the minimum requirement of Vitamin A from the mixture of X and Y is 10 units, each of which contains 1 unit and 2 units of Vitamin A respectively.

⟹ 2x + 2y ≥ 12

i.e. the minimum requirement of Vitamin B from the mixture of X and Y is 12 units, each of which contains 2units of vitamin B each.

⟹ 3x + y ≥ 8

i.e. the minimum requirement of vitamin C from the mixture of X and Y is 8 units, each of which contains 3 units and 1 unit of vitamin C respectively.

Hence, the mathematical formulation of the LPP is as follows :

Find ‘x’ and ‘y’ that:

Minimises Z = 16x + 20y

Subject to the following constraints:

(i) x + 2y ≥ 10

(ii) 2x + 2y ≥ 12

i.e. x + y ≥ 6

(iii) 3x + y ≥ 8

(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 C(2,4)

Let us consider 16x + 20y ≤ 112

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

The minimum cost of the mixture is ₹112.

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