Question

The corner points of the feasible region are $A(0,0),B(16,0),C(8,16)$ and $D(0,24)$. The minimum value of the objective function $z=300x+190y$ is _______

• A. $5440$
• B. $4800$
• C. $4560$
• D. $0$

Answer 1

The correct option is D $0$

We know that, for a cartesian polygon , the maximum value occurs at the corner points or vertices of the polygon.

Given $z=300x+190y$

By substituting $A(0,0)$ in the equation we get $z=0$

By substituting $B(16,0)$ in the equation we get $z=4800$

By substituting $C(8,16)$ in the equation we get $z=5440$

By substituting $D(0,24)$ in the equation we get $z=4560$

Hence the minimum value of Z occured at $C(0,0)$ with $z=0$