Answer:
Option A is correct .i.e., ( 0, 0 ) , ( 0, 3) , ( 2, 3 ) & ( 5, 0)
Step-by-step explanation:
Given constraints are
x + y ≤ 5 , y ≤ 3 , x ≥ 0 & y ≥ 0
To find Vertex of Feasible region we find point of intersection of lines.
To find Point of intersection we replace sign of inequality with equality.
So,
Point of intersection of x + y = 5 , y = 3
put y = 3 in another equation, we get
x + 3 = 5
⇒ x = 5 - 3
⇒ x = 2
⇒ Point of intersection or vertex = ( 2 , 3 )
Point of intersection of y = 3 , x = 0
⇒ Point of intersection or vertex = ( 0 , 3 )
Point of intersection of x + y = 5 , y = 0
put y = 0 in another equation, we get
x + 0 = 5
⇒ x = 5
⇒ Point of intersection or vertex = ( 5 , 0 )
Point of intersection of x = 0 , y = 0
⇒ Point of intersection or vertex = ( 0 , 0 )
Point of intersection of x + y = 5 , x = 0
put x = 0 in another equation, we get
0 + y = 5
⇒ y = 5
⇒ Point of intersection = ( 0 , 5 ) but this is not required vertex as it lie on the above of y = 3
Therefore, Option A is correct .i.e., ( 0, 0 ) , ( 0, 3) , ( 2, 3 ) & ( 5, 0)