Answer:
A(0,10)
Step-by-step explanation:
Given the 4 inequalities: 
s ≥ 12 - 0.5t (1)
s ≥ 10 -t (2)
s ≤ 20-t (3) 
s ≥ 0
t ≥ 0
Let analyse all 4 possible answer: 
Let substitute this point into (1) we have: 10 ≥ 12 -0.5*0 Wrong 
We do not choose A 
Let substitute this point into (1) we have: 20 ≥ 12 -0.5*0  True 
Let substitute this point into (2) we have: 20 ≥ 10 - 0 True 
Let substitute this point into (3) we have: 20 ≤ 20 - 0 True 
We choose B as the vertex 
Let substitute this point into (1) we have: 16 ≥ 12 -0.5*4  True 
Let substitute this point into (2) we have: 16 ≥ 10 - 4 True 
Let substitute this point into (3) we have: 16 ≤ 20 - 4 True 
We choose C as the vertex 
Let substitute this point into (1) we have: 4 ≥ 12 -0.5*16 True 
Let substitute this point into (2) we have: 4 ≥ 10 - 16 True 
Let substitute this point into (3) we have: 4 ≤ 20 - 16 True 
We choose B as the vertex 
Hence, the point A(0,10)  is not one of the vertices of the shaded region of the  set of inequalities.