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