The company makes concrete bricks made up of cement and sand. The weight of a concrete brick has to be least 5 kg. Cement costs Rs 20 per kg.
The company makes concrete bricks made up of cement and sand. The weight of a concrete brick has to be least 5 kg. Cement costs Rs 20 per kg. and sand costs of Rs 6 per kg. strength consideration dictate that a concrete brick should contain minimum 4 kg. of cement and not more than 2 kg. of sand. Form the L.P.P. for the cost to be minimum.
1 Answers
Let the company use x1 kg of cement and x2 kg of sand to make concrete bricks.
Cement costs Rs 20 per kg and sand costs Rs 6 per kg.
∴ the total cost c = Rs (20x1 + 6x2)
This is a linear function which is to be minimized.
Hence, it is the objective function. Total weight of brick = (x1 + x2) kg
Since the weight of concrete brick has to be at least 5 kg,
∴ x1 + x2 ≥ 5.
Since concrete brick should contain minimum 4 kg of cement and not more than 2 kg of sand,
x1 ≥ 4 and 0 ≤ x2 ≤ 2
Hence, the given LPP can be formulated as : Minimize c = 20x1 + 6x2, subject to x1 + x2 ≥ 5, x1 ≥ 4, 0 ≤ x2 ≤ 2.