Question

Kellogg is a new cereal formed of a mixture of bran and rice, that contains at least 88 grams of protein and at least 36 milligrams of iron. Knowing that bran contains 80 grams of protein and 40 milligrams of iron per kilograms, and that rice contains 100 grams of protein and 30 milligrams of iron per kilogram, find the minimum cost producing this new cereal if bran costs ₹5 per kilogram and rice costs ₹4 per kilogram.

Answer 1

Let x and y be number of kilograms of bran and rice.

∴According to the question,

80x + 100y ≥ 88, 40x + 30y ≥ 36, x ≥ 0, y ≥ 0

Minimize Z = 5x + 4y

The feasible region determined 80x + 100y ≥ 88, 40x + 30y ≥ 36, x ≥ 0, y ≥ 0 is given by

The feasible region is unbounded. The corner points of feasible region are A(0,1.2) , B(0.6,0.4) , C(1.1,0).

The value of Z at corner points are

Corner Point	Z = 5x + 4y
A(0, 1, 2)	4.8
B(0, 6, 0.4)	4.6	Minimum
C(1.1, 0)	5.5

The minimum value of Z is 4.6 at point (0.6,0.4).

Hence, the diet should contain 0.6 kgs of bran and 0.4 kgs of rice for achieving minimum cost of Rs.4.6.