# Linear Programming

## Class 12 NCERT

### NCERT

1   Maximise $Z = 3x + 4y$ Subject to the constraints: $x + y \leq 4, x \geq 0, y \geq 0$

##### Solution :

The feasible region determined by the constraints, $x + y \leq 4, x \geq 0, y \geq 0$, is as follows.$\\$ The corner points of the feasible region are $O ( 0, 0 ), A ( 4, 0 )$ , and $B ( 0, 4 )$ .$\\$ The values of $Z$ at these points are as follows.$\\$ table $\\$ Therefore, the maximum value of $Z$ is $16$ at the point $B ( 0, 4 )$

##### Solution :

The feasible region determined by the constraints, $x + 2y \leq 10,3x + y \leq 15, x \geq 0$ and $y \geq 0$ , is as follows.$\\$ The corner points of the feasible region are $A (5, 0), B (4, 3),$and $C (0, 5).$$\\$ The values of $Z$ at these corner points are as follows.$\\$ table $\\$ Therefore, the maximum value of $Z$ is $18$ at the point $(4, 3).$