The corner points of the feasible region determined by system of linear constraints are (60, 0), (120, 0), (40, 20) and (60, 30). Let $z = ax + by, a, b>0$ be the objective function. Find condition on a and b so that the maximum of $z$ occurs at (120, 0) and (60, 30).

$2a=b$

objective function $z = ax + by$

Maxima occurs at two points (120, 0) and (60, 30)

$⇒z(120, 0)=z(60, 30)$

$⇒120a+0=60a+30b$

$⇒120a=60a+30b$

$60a=30b$

$2a=b$