The feasible region corresponding to the linear constraints of a Linear Programming Problem (LPP) is represented by the shaded region in the given figure. Which of the following is not a constraint to the given LPP?

The feasible region shows the area where all constraints are satisfied. The task is to find which option is not a constraint, meaning it doesn't form a boundary of this shaded region.

---

Each constraint creates a boundary line. If a constraint is part of the LPP, the shaded region will be on the correct side of that line.

---

Testing $x + 2y \leq 10$:

This forms the upper boundary of the feasible region. Points in the shaded region satisfy this inequality (they're below or on this line). This is a constraint.

---

Testing $x + y \geq 2$:

This forms the lower-left boundary of the feasible region. Points in the shaded region satisfy this inequality (they're above or on this line). This is a constraint.

---

Testing $x - y \leq 1$:

This forms another boundary of the feasible region. Points in the shaded region satisfy this inequality. This is a constraint.

---

Testing $x - y \geq 1$:

This is the opposite of $x - y \leq 1$. If the feasible region satisfies $x - y \leq 1$, it cannot also satisfy $x - y \geq 1$. These two constraints contradict each other.

The line $x - y = 1$ forms a boundary, but the feasible region is on the side where $x - y \leq 1$, not where $x - y \geq 1$.

Since the feasible region cannot be on both sides of the same line, only one of these can be a constraint. From the graph, the feasible region satisfies $x - y \leq 1$, not $x - y \geq 1$.

---

Therefore, $x - y \geq 1$ is not a constraint to the given LPP.