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
⟹ 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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