CUET Mathematics 2025 21 May Shift 1 PYQs

For the linear programing problem,

$Minimize(Z) = 60x + 30y$

subject to: $2x - y \geq -5; 3x + y \geq 3; 2x - 3y \leq 12; x, y \geq 0$

the optimal value of $z$ is

Let the corner points of the bounded feasible region of the linear programming problem (LPP) $Z = ax+by$ be: (0, 0), (2, 0), (20/19, 45/19) and (0, 3). If the optimal value of Z occurs at both points (2, 0) and (20/19, 45/19), then the relation between a and b is:

The corner points of the bounded feasible region determined by a set of constraints in an LPP are P(0, 5), Q(3, 5), R(5, 0) and S(4, 1). If the objective function is $z = ax + 2ay$, where $a, b > 0$ then the condition on $a$ and $b$ such that the maximum value of z occurs at Q and S is