Maths. Section ALinear Programming

The feasible region for the constrains x ≥ 0, x+y ≤ 1 and x-y ≤ 1, is…

The feasible region for the constrains $x ≥ 0, x+y ≤ 1$ and $x-y ≤ 1$, is situated in :

(A) I and II Quadrant
(B) I Quadrant
(C) II and IV Quadrant
(D) IV Quadrant
(E) I, II, III and IV Quadrant

Choose the correct answer from the options given below :

Answer & explanation

Correct answer: option 2

x ≥ 0 ⇒ solution is above y-axis → possibly in I or IV quadrant

Plotting

x - y = 1

x	1	0
y	0	-1

x + y = 1

x	1	0
y	0	1

Checking O(0, 0)

for x - y ≤ 1 ⇒ 0 ≤ 1

→ solution lies to side containing O(0, 0)

for x + y ≤ 1 ⇒ 0 ≤ 1

→ solution lies to side containing O(0, 0)

⇒ Solution region in 1^st and 4^th quadrant