The corner points of the feasible region determined by the set of constraints (linear inequalities ) are P(0, 5), Q(3, 5), R(5, 0) and S(4, 1) and the objective function $z=ax+2by $ where a, b > 0. The condition on a and b such that maximum z occurs at Q and S is :

a-8b=0

The correct answer is Option (4) → $a-8b=0$

for maximum to occur both on Q and S

$Z_Q=Z_S$

so $3a+10b=4a+2b$

so $a-8b=0$