The shaded region in the following figure represents the solution… - Vidyadip

MCQ

The shaded region in the following figure represents the solution set for a certain linear programming problem. Then, linear constraints for this region are given by

A
$2 x+3 y \geq 6,-x+2 y \geq 2,3 x+6 y \leq 18,5-3 y \geq$ $3, x \geq 0, y \geq 0$
B
$2 x+3 y \geq 6,-x+2 y \leq 2, x-3 y \leq 3,2 y \geq 18$, $x \geq 0, y \geq 0$
C
$2 x+3 y \leq 6,-x+2 y \geq 2,3 x+6 y \leq 18, x-3 y \leq$ $3, x<0, y<0$
D
$2 x+3 y \geq 6,3 x+6 y \leq 18, x-3 y \leq 3,-x+2 y \leq 2$, $x \geq 0, y \geq 0$

✓

Answer

Line $L_1$ passes through $(0,3)$ and $(6,0)$
$\therefore \quad$ Equation of line $L_1$ is $3 x+6 y=18$

The shaded region for $L_1$ lies on the side of origin.
So, inequality will be $3 x+6 y \leq 18$.
Similarly $L_2$ represent the line $2 x+3 y=6$
Since shaded region lies on opposite side of origin for $L_2$
$
\therefore \quad 2 x+3 y \geq 6
$ Similarly, other two inequalities are: $-x+3 y \geq 3$ or $x-3 y$ $\leq 3$ represented by $L_4$, and $-x+2 y \leq 2$ represented by $L_3$.
So the given system of inequations are $2 x+3 y \geq 6$,
$
3 x+6 y \leq 18, x-3 y \leq 3,-x+2 y \leq 2 x, y \geq 0
$

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