If the objective function for a linear programming problem (LPP) is $Z = 4x + 5y$ and the corner points of the bounded feasible region are (9, 0), (4, 3), (2, 5), and (0,8), then the minimum value of Z is:

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

The feasible region associated with the inequality $2x + 3y > 4$ is

The corner points of the bounded feasible region of a linear programming problem are A(15,0), B(40,0), C(4, 18), D(6, 12) and objective function is $z = 20x+10y$, then which of the following are TRUE?

(A) Value of z at point A(15, 0) = 300.

(B) Value of z at point B(40, 0) = 800.

(C) Value of z at point C(4, 18) = 340.

(D) Maximum value of z = 800.

Choose the correct answer from the options given below:

For linear programming problem maximize $z=2x+3y$

Subject to the constraints $x+y \leq 4$

$x \leq 2$

$x \geq 0, y \geq 0$

Maximum value of z is

If corner points of the bounded feasible region of a linear programming problem are as in the figure given below and $z = px + qy$, $(p,q > 0)$ is an objective function. Then the relation between $p$ and $q$, when $z$ is maximum at $D(4,10)$ and $C(6,8)$, is:

The optimal value of linear programming problem maximum $Z = 3x + 4y$, subject to,

$x + 3y \leq 12$

$x + y \geq 8$

$x, y \geq 0$ is