Are you sure some of those first three ≤'s shouldn't have been ≥ ?.
The graph seems funny because the first two restraints are irrelevant,
So the feasible region is on or below all three lines, which means it's
just on or below the green shaded region below the bottom line.



That means there are only three corner points

(0,0), (0,6), and (8,0)

Substituting (x,y) = (0,0) in z = 200x+100y,
z = 200(0)+100(0) = 0 + 0 = 0

Substituting (x,y) = (0,6) in z = 200x+100y,
z = 200(0)+100(6) = 0 + 600 = 600

Substituting (x,y) = (8,0) in z = 200x+100y,
z = 200(8)+100(0) = 1600 + 0 = 1600

So the maximum value for z is 1600 when x = 8 and y = 0.

Edwin