CBSE Guess > Papers > Important Questions > Class XII > 2010 > Maths > Mathematics By Mr. M.P.Keshari

Linear Programming

Q.10. 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 kilogram, and that rice contains 100 grams of protein and 30 milligrams of iron per kilogram, find the minimum cost of producing this new cereal if bran costs Rs5 per kilogram and rice costs Rs4 per kilogram.

Solution :

Let the cereal contains x kg of bran and y kg of rice. Clearly x ≥ 0 and y ≥ 0.
According to the hypothesis the linear programming problem is :
Minimize Z = 5x + 4y
Subject to the constraints :
(80/1000) x + (100/1000) y ≥ (88/1000)
Or, 20 x + 25 y ≥ 22 ----------------- (1)
And (40/1000) x + (30/1000) y ≥ (36/1000)
Or, 20 x + 15 y ≥ 18 ------------------ (2)
And also x ≥ 0, y ≥0 ------------------- (3)
Now the lines 20 x + 25 y = 22 and 20x + 15 y = 18 are drawn.

Fig

These lines meet at E (0.6, 0.4). The feasible region is shaded and it is an unbounded region with vertices A (1.1, 0), E (0.6, 0.4) and D (0, 1.2).

Therefore, minimum cost of producing this cereal is Rs4.60 per kg. [Ans.]

Q.11. A new cereal, formed of a mixture of bran and rice, 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 kilogram, and that rice contains 100 grams of protein and 30 milligrams of iron per kilogram, find the minimum cost of producing a kilogram of this new cereal if bran costs Rs. 28 per kilogram and rice costs Rs. 25 per kilogram.

Solution : – Do yourself. [Ans. = Rs. 26.8]

Paper By Mr. M.P.Keshari
Email Id : [email protected]
Ph No. : 09434150289