The above information can be expressed using the following table:
Let the amount of Bran and Rice required be ‘x’ and ‘y’ kgs respectively.
Cost of Bran = 5x
Cost of Rice = 4y
Cost of the cereal = 5x + 4y
⟹ 80x + 100y ≥ 88
i.e. the minimum requirement of protein in the cereal, from Bran and Rice combined, is 88g, each of which have 80g and 100g of proteins respectively.
⟹ 40x + 30y ≥ 36
i.e. the minimum requirement of iron in the cereal, from Bran and Rice combined, is 36mg, each of which have 40mg and 30mg of iron.
Hence, mathematical formulation of LPP is as follows:
Find ‘x’ and ‘y’ that:
Minimises Z = 5x + 4y
Subject to the following constraints:
(i) 80x + 100y ≥ 88
(ii) 40x + 30y ≥ 36
(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 B(0.6,0.4)
Let us consider 5x + 4y ≤ 4.6
As it has no intersection with the feasible region, the smallest value is the minimum value.
The minimum cost of the cereal is ₹4.6
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