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.