The minimum value of $z = 3x + 2y$ subjected to the constraints $2x + y \geq 7, x + 2y \geq 8, x, y \geq 0$ is

If the feasible region of an LPP is bounded and the corresponding objective function is $z = 5x - 9y$, then the objective function attains:

The sum of the x-coordinates of the corner points of the feasible region for the LPP: Minimize $z = 3x + 2y$ subject to constraints $x + y \leq 14$, $x \geq 4$, $x \leq 8, y \geq 0$ is

Which of the following is NOT a basic requirement of the linear programming problem (LPP)?

Corner points of the bounded feasible region determined by the system of linear constraints are (0, 3), (1, 1), and (3, 0). Let $Z = px+qy$, where $p,q>0$. Condition on $p$ and $q$ so that the minimum of Z occurs at (3, 0) and (1, 1) is

In the given figure, feasible region represented by the constraints $4x + y \geq 80$, $x + 5y \geq 115$, $3x + 2y \leq 150$, $x,y \geq 0$ is

The corner points of the bounded feasible region determined by the system of linear constraints 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 the maximum of Z occurs at both (5, 0) and (3, 4) is