List of top Mathematics Questions on Linear Programmig Problem asked in CUET (UG)

The corner points of the feasible region determined by $x + y \leq 8$, $2x + y \geq 8$, $x \geq 0$, $y \geq 0$ are $A(0, 8)$, $B(4, 0)$, and $C(8, 0)$. If the objective function $Z = ax + by$ has its maximum value on the line segment $AB$, then the relation between $a$ and $b$ is:

Which one of the following represents the correct feasible region determined by the following constraints of an LPP?
\[ x + y \geq 10, \quad 2x + 2y \leq 25, \quad x \geq 0, \quad y \geq 0 \]