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
⟹ 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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