Question

Kellogg is a new cereal formed from a mixture of bran and rice that contains at least 88 gm of protein and at least 36 milligram of iron per kg knowing that bran contains 80 gm of protein and 40 milligram of iron per kilogram and that rice contains 100 gm of protein and 30 milligram of iron per kilogram, find the minimum cost of producing this new cereal if bran cost Rs 5 kilogram and rice cost Rs 4 per kilogram.

Answer 1

Let the units of Bran be x kg & Rice be y kg

Minimize Z = 5x + 4y 

subject to the constraints 

80x + 100y ≥ 88 

40x + 30 

y ≥ 36 

x, y ≥ 0

z is minimum at B (\(\frac{3}{5}, \frac{2}{5}\))

Z_min = 4.6