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

$a-8b=0$

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

Given: Objective function $z = ax + 2by$.

For $z$ to attain maximum value at both points Q(3,5) and S(4,1), we must have:

$z_Q = z_S$

$\Rightarrow a(3) + 2b(5) = a(4) + 2b(1)$

$\Rightarrow 3a + 10b = 4a + 2b$

$\Rightarrow -a + 8b = 0$

$\Rightarrow a - 8b = 0$

Hence, the required condition is: $a - 8b = 0$.