The corner points of the feasible region determined by

x + y ≤ 8, 2x + y ≥ 8, x ≥ 0, y ≥ 0

are A(0, 8), B(4, 1) and C(8, 0). If the objective function Z = ax + by has its maximum value on the line segment AB, then the relation between a and b is:

7b = 4a

The correct answer is Option (2) → 7b = 4a

corner points

$A(0, 8), B(4, 1),C(8, 0)$

$Z = ax + by$

$Z_A=Z_B$

$8b=4a+b$

so $7b=4a$