1 \(x, y \geq 0 ; x-y \geq 0 ; x \leq 5: y \leq 3\)
2 \(x, y \geq 0 ; x+y \geq 0 ; x \geq 5 ; y \leq 3\)
3 \(\mathrm{x}, \mathrm{y} \geq 0 ; \mathrm{x}-\mathrm{y} \leq 0 ; \mathrm{x} \leq 5 ; \mathrm{y} \leq 3\)
4 \(\mathrm{x}, \mathrm{y} \geq 0 ; \mathrm{x}-\mathrm{y} \geq 0 ; \mathrm{x} \leq 5 ; \mathrm{y} \geq 3\)
Explanation:
(A) : Given the figure,

Accordingl to the figure, \(\mathrm{OC}\) line passes through \((0,0)\) and \((3,3)\).
Now, the equation of line is \(y=x\)
Then, the shaded protion of this line is towards the Xaxis, so \(x-y \geq 0\) in the given figure, linel \(A B\) is parallel to \(\mathrm{Y}\)-axis.
Therefore, The equation of line \(\mathrm{AB}\) is \(\mathrm{x}=5\) also the shaded portion of this line is towards the origin, so, \(x-5 \leq 0\) or \(x \leq 5\).
In the given figure, line \(\mathrm{BC}\) is parallel to \(\mathrm{X}\)-axis.
\(\therefore\) The equation of line \(\mathrm{BC}\) is \(\mathrm{y}=3\).
Also, the shaded portion of this line is towards the origin,
so, \(\mathrm{y}-3 \leq 0\) or \(\mathrm{y} \leq 3\).
So, the shaded region line in the firstl quadrant,
so, \(\mathrm{x} \geq 0\) and \(\mathrm{y} \geq 0\).
\(\because\) Constraints of given shaded region are
\(x \geq 0, y \geq 0, x-y \geq 0, x \leq 5, y \leq 3\).