The shaded unbounded area of an LPP is the result of constraints:

The correct answer is Option (4) → \( x\le 8,y-x\ge 5;x,y\ge 0 \)

The boundary line passes through (0, 5) and (8, 13). Its slope is \( \frac{13-5}{8-0}=1 \), so its equation is

    \( \displaystyle y=x+5,\ \text{i.e.}\ y-x=5 \)

The shaded region lies above this line. The point (0, 10) is inside it, and \( 10-0=10\ge 5 \). So the region satisfies \( y-x\ge 5 \).

The shaded region lies to the left of the vertical line x = 8 and to the right of the y-axis, so \( x\le 8 \) and \( x\ge 0 \). It is also above the x-axis, so \( y\ge 0 \).

The constraints are \( x\le 8,\ y-x\ge 5;\ x,y\ge 0 \).