Which one of the following set of constraints does the given shaded r…

The correct answer is Option (1) → $x + y ≤ 30,x+y≥ 15,x ≤ 15, y ≤20,x,y ≥0$

The boundary lines visible in the figure are identified as follows

The descending line passing through $(0,30)$ and $(30,0)$ is

$x+y=30$

The parallel descending line passing through $(0,15)$ and $(15,0)$ is

$x+y=15$

The vertical boundary is at

$x=15$

The horizontal boundary is at

$y=20$

The shaded region lies to the right of the $y$-axis and above the $x$-axis

$x\ge 0,\; y\ge 0$

The region is between the two parallel lines

$x+y\ge 15$ and $x+y\le 30$

It is also bounded by

$x\le 15$ and $y\le 20$

The given shaded region represents the constraints $x+y\le 30,\; x+y\ge 15,\; x\le 15,\; y\le 20,\; x\ge 0,\; y\ge 0$.