Question

The company makes concrete bricks made up of cement and sand. The weight of a concrete brick has to be at least 5 kg. Cement costs $\square$20 per kg and sand costs of $\square$6 per kg. Strength consideration dictates that a concrete brick should contain minimum 4 kg of cement and not more than 2 kg of sand. Form the LPP for the cost to be minimum.

Answer 1

Let the company use $x_1$ kg of cement and $x_2$ kg of sand to make concrete bricks.
Cement cost $squqre$ 20 per kg and sand cost $\square$ 6 per kg.
$\therefore$ the total cost c = $\square (20x_1+6x_2)$
This is a linear function which is to be minimized
Hence, it is an objective function.
Total weight of brick = $(x_1+x_2)kg$
Since, the weight of concrete bricks has to be at least 5 kg,
$\therefore x_1+x_2\le 5$
Since concrete brick should contain minimum 4 kg of cement and not more than 2kg of sand,
$x_1\ge 4and0\le x_2\le 2$
Hence, the given LPP can be formulated as:
Minimize $c=20x_1+6x_2$, subject to
$x_1+x_2\ge 5,x_1\ge 4,0\le x_2\le 2$