Question

Which one of the following point is not in a feasible region bounded by the inequalities $x \leq 4$, $y \leq 6$, $x + y \leq 6$, $x \geq 0$, $y \geq 0$

• A. $(0,0)$
• B. $(4,0)$
• C. $(4,2)$
• D. $(0,6)$
• E. $(6,0)$

Hint:

For feasible region questions: - Check each inequality one by one - Even if one fails, the point is not feasible

Answer 1

Answer: (E)

Concept: A feasible region consists of all points satisfying given inequalities. A point is feasible if it satisfies all constraints.

Step 1: List the constraints.
\[ x \leq 4,\quad y \leq 6,\quad x + y \leq 6,\quad x \geq 0,\quad y \geq 0 \]

Step 2: Check each option.
(A) $(0,0)$: \[ 0 \leq 4,\; 0 \leq 6,\; 0+0 \leq 6 \Rightarrow \text{Valid} \] (B) $(4,0)$: \[ 4 \leq 4,\; 0 \leq 6,\; 4+0 \leq 6 \Rightarrow \text{Valid} \] (C) $(4,2)$: \[ 4 \leq 4,\; 2 \leq 6,\; 4+2 = 6 \Rightarrow \text{Valid} \] (D) $(0,6)$: \[ 0 \leq 4,\; 6 \leq 6,\; 0+6 = 6 \Rightarrow \text{Valid} \] (E) $(6,0)$: \[ 6 \nleq 4 \Rightarrow \text{Not valid} \]

Step 3: Conclusion.
The point $(6,0)$ does not satisfy $x \leq 4$.