The corner points (vertices) of the feasible region are found where two constraint lines intersect or where a constraint line meets an axis.
Given constraints:
2x−y≤−5 which gives y≥2x+5
3x+y≥3 which gives y≥3−3x
2x−3y≤12 which gives y≥32x−12
x≥0,y≥0
For points on the y-axis, set x=0:
From y≥2(0)+5:
y≥5
Boundary point: (0,5)
From y≥3−3(0):
y≥3
Boundary point: (0,3)
From y≥32(0)−12:
y≥−4
This does not restrict y further in the first quadrant.
For points on the x-axis, set y=0:
From 2x−0≤−5:
x≤−2.5
This is not possible since x≥0.
From 3x+0≥3:
x≥1
Boundary point: (1,0)
From 2x−3(0)≤12:
x≤6
Boundary point: (6,0)
The corner points of the feasible region are:
(0,3)
(0,5)
(1,0)
(6,0)