CUET Mathematics 2023 30 May Shift 3 PYQs

An objective function $z = ax + by$ is maximum at points (15,15) and (0, 20). If $a, b \geq 0$ and $ab = 27$, then the maximum value of the objective function is

The maximum value of the objective function $z = 10x + 15y$ of an L.P.P. subjected to the constraints

$2x + 4y \leq 8$,

$3x + y \leq 6$,

$-x - y \geq -4$,

$x \geq 0$, $y \geq 0$ is:

The corner points of the bounded feasible region determined by the system of linear inequalities are $(0, 0)$, $(2, 4)$, $(0, 5)$ and $(4, 0)$. If the maximum value of $z = ax + by$, where $a, b > 0$ occurs at both $(2, 4)$ and $(4, 0)$, then