The corner points of the bounded feasible region determined by $2x+y \leq 10$, $x+3y \leq 15$, $x,y \geq 0$ are (0, 0), (5, 0), (3, 4) and (0, 5). Let $z = px+qy$, $p,q > 0$, then the relation between $p$ and $q$ so that the maximum of $z$ occurs at both (3, 4) and (0, 5), is

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

Objective function of LPP is:

The maximum value of $z=5x+3y$ subjected to the constraints $2x+3y \ge 60, 2x+y \le 40; x,y \ge 0$ is:

The corner points of the feasible region determined by the following system of linear inequalities :

$2x + y \leq 10$, $x + 3y \leq 15$, $x, y \geq 0$ are (0, 0), (5, 0), (3, 4) and (0, 5). Let $z = px + qy$, where $p, q > 0$ condition on p and q so that maximum of z occurs at both (3, 4) and (0, 5) is :

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

If the corner points of the bounded feasible region for a Linear Programming Problem (LPP) are A(0,2), B(3, 0), C(2, 3) and D(3, 1), then the maximum value of the objective function $Z = 4x + 2y$ occurs at