The corner points of the feasible region of LPP $x+y ≤ 200, y ≥ 4 x, x ≥ 20, x ≥ 0, y ≥ 0$ are :
(A) $(20,180)$
(B) $(40,180)$
(C) $(20,80)$
(D) $(40,80)$
(E) $(40,160)$
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 1
$x \geq 0, y \geq 0$ → graph lies in first quadrant
first to plot lines y = 4x, x + y = 200, x = 20
y = 4x
| x | 0 | 40 |
| y | 0 | 160 |
x + y = 200
| x | 0 | 200 |
| y | 200 | 0 |
x = 20
for y ≥ 4x
checking for random point (20, 100)
→ 100 ≥ 80
so the side of line at which it lies is solution region
for x + y ≤ 200
checking for (0, 0)
⇒ 0 ≤ 200
hence side at which (0, 0) lies is solution region
at and taking intersection region to get possible region, we get following corner points
(20, 180) (20, 80) (40, 160)
A, C and E