In a LPP constraints are 3x + y ≤ 9, x + y ≤ 5, x ≥ 0, y ≥ 0 and objective function max (z) = x + 2y. Which point doesn't lie in feasible region?

(5, 2)

The correct answer is Option (4) → (5, 2)

$\text{Check } (1,1):\ 3(1)+1=4 \le 9,\ 1+1=2 \le 5 \Rightarrow \text{feasible}$

$\text{Check } (2,1):\ 3(2)+1=7 \le 9,\ 2+1=3 \le 5 \Rightarrow \text{feasible}$

$\text{Check } (2,3):\ 3(2)+3=9 \le 9,\ 2+3=5 \le 5 \Rightarrow \text{feasible}$

$\text{Check } (5,2):\ 3(5)+2=17 > 9 \Rightarrow \text{not feasible}$

$\text{Point not in feasible region} = (5,2)$