Consider the linear programming problem Maximise $z=3 x+y$ subject to constraints $x+y ≤ 6, x ≥ 0, y ≥ 0$. Which of the following statements are true?

A. $x ≥ 0, y ≥ 0$ are non negative restrictions.
B. The point $(1,1)$ does not lie in the half plane $x+y ≤ 6$.
C. There are 2 corner points of the feasible region of given LPP.
D. Maximum value of $z=18$

Choose the correct answer from the options given below:

A and D only

The correct answer is Option (1) - A and D only

$Z=3x+y$

A → True

B → false, (1, 1) lies in half plane

C → false, three corner point exist

D → $Z_0=0$

$Z_A=6$

$Z_B=18$ (True)