The feasible region is in the square ABCD. As can be seen from the figure, when x=2 and y= 1, z takes the maximum value, that is, 2/a+ 1/b=5.

8a+b =(8a+b)*(2/a+ 1/b)/5 =( 17+2b/a+8a/b)/5、？ Using the important inequality, we can know that its minimum value is 5.

2, 0 or -8

The line where MN is located is perpendicular to the line y=x+m, which can be set as y=-x+t,

Combining hyperbola and eliminating x, we get 2x 2+2tx-t2-3 = 0.

Let m (x 1, y 1) and n (x2, y2).

x 1+x2=-t

So y1+y2 =-(x1+x2)+2t = 3t.

So the midpoint is (-t/2, 3t/2). If you change it to y 2 =18x, you get (3t/2)2 = 18 *(t/2).

Solution: t=0 or -4.

So the midpoint is (0,0) or (2,6).

Substitute y=x+m to get m=0 or -8.