Which among the following is NOT a corner point of the LPP, maximize Z = 4x + y subject to the constraints $$x + y \le 50, 3x + y \le 90, x \ge 0, y \ge 0 ?$$​​

Correct option is C

Given:
Constraints:
​$$x + y \le 50\\3x + y \le 90\\x \ge 0, y \ge 0$$​​
Formula used:
Corner points are obtained by intersections of boundary lines and axes
that satisfy all constraints.
Solution:
Check feasible corner points:
Intersection with y-axis:
x = 0
From x + y = 50 => (0, 50)
From 3x + y = 90 => (0, 90) (not feasible since x + y > 50)
Intersection with x-axis:
y = 0
From x + y = 50 => (50, 0)
From 3x + y = 90 => (30, 0)
Intersection of the two lines:
x + y = 50
3x + y = 90
Subtracting:
2x = 40 => x = 20
y = 30
Thus corner points are:
(0, 0), (0, 50), (20, 30), (30, 0)
Now check options:
(0, 50) yes
(20, 30) yes
(50, 0) no (violates $$3x + y \le 90$$​)
(30, 0) yes
The correct answer is (c) (50, 0).