Which of the following is a vertex of positive region bounded by the inequalities : $4x+y ≥80; 2x+y ≥60; x, y ≥ 0$

(0, 30) (80, 0) (40, 10) (10, 40)

(10, 40)

The correct answer is Option (4) → (10, 40) plotting $4x+y=80$   x     20     0   y 0 80 $2x+y=60$   x     30     0   y 0 60 Point of intersection  $4x+y=80$    ...(1) $2x+y=60$   ...(2) eq. (1) - eq. (2) $4x+y-22x-y=80-60$ $2x=20$ $x=10$ from (1) $20x+y=60$ $y=40$ (10, 40) is one such vertex