The linear programming problem :

minimise  z = 3x + 2y

subject to the constraints

x + y ≥ 8,

3x + 5y ≤ 15, x ≥ 0, y ≥ 0

has

no feasible solution

Z = 3x + 2y

constraints

x + y ≥ 8

3x + 5y ≤ 15

x, y ≥ 0 → solution lies in 1^st quadrant

Solving for first

x + y = 8

3x + 5y = 15

Checking for point O(0, 0)

for: x + y ≥ 8

⇒ 0 ≥ 8 (false)

solution lies to side of x + y = 8 not containing O(0, 0)

for: 3x + 5y ≤ 15

⇒  0 ≤ 15

solution lies to side of 3x + 5y = 15 containing O(0, 0)

⇒ No feasible region