Given:
T=X - 3Y
To find the vertex which will result in the minimum value of the function:
Let us check the options one by one.
A. Given: (4,4)
On substitution, we get
T=4-3(4)
T=4-12
T=-8
B. Given: (0,1)
On substitution, we get
T=0-3(1)
T=-3
C. Given: (4,1)
On substitution, we get
T=4-3(1)
T=4-3
T=1
D. Given: (0,4)
On substitution, we get
T=0-3(4)
T=0-12
T=-12
T=-12 is the minimum value.
Hence, (0,4) is the vertex that will result in the minimum value of the function.
Therefore, the correct option is D.