Choose the wrong statement from the following :

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:

The corner points of the bounded feasible region for an LPP are (0, 20), (3,12), (6,8), and (0,15). The objective function is $Z = \alpha x + \beta y$, where $\alpha, \beta > 0$. If the maximum of Z occurs at the corner points (3,12) and (6,8), then the relationship between $\alpha$ and $\beta$ 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 region represented by the constraints $x \geq 0, y \geq 0$ of an LPP is

The feasible region of an LPP Max $Z = 3x + 2y$ subject to $x \geq 0, y \geq 0, x - 2y \leq 3$ is:

The minimum value of $Z = 2x + y$ subjected to $x + y \geq 10, 2x + 3y \leq 26, x, y \geq 0$ is