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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