The corner points of the bounded feasible region for an LLP are: (5, 5), (15, 15), (0, 20) and (0, 10). Let $z=3x+9y$ be the objective function. Then the value of maximum (z) - minimum (z) is

120

The correct answer is Option (3) → 120

Compute $z=3x+9y$ at each corner point.

At $(5,5):\ z=3(5)+9(5)=15+45=60$

At $(15,15):\ z=3(15)+9(15)=45+135=180$

At $(0,20):\ z=3(0)+9(20)=0+180=180$

At $(0,10):\ z=3(0)+9(10)=0+90=90$

Maximum $z=180$, Minimum $z=60$

The value of maximum$(z)$ − minimum$(z)$ is $120$.