For a LPP, maximize $z=2x+3y$, subjected to constraints:

$x\ge2, x\le7, y\le x, x+y\le10, x\ge0, y\ge0$

Which of the following statements are TRUE ?

(A) Vertices of feasible region are (2, 0), (7, 0), (7, 3), (5, 5) and (2, 2).

(B) Maximum $z=25$ at point (5, 5).

(C) Maximum $z=25$ at infinite numbers of points.

(D) The feasible region is unbounded.

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The linear constraints, for which the shaded area in the figure is the feasible region of an LPP, are :

For the linear programming problem (LPP):

Maximize $Z = x + 1.5y$, subject to constraints,

$x + 2y \leq 40$, $2x + y \leq 40$, $x + y \leq 25$, $x \geq 0$, $y \geq 0$.

Which of the following is NOT correct?

If the corner points of the bounded feasible region for an LPP are $(5,0), (0,4), (0,2), (3,4)$, and $(0,7)$, then the minimum value of the objective function $z = 2x+5y$ occurs at :

The corner points of the feasible region of a LPP are (0,2), (3,0), (6,0), (6,8) and (0,5). If the objective function is $z = 4x + 6y$, then the sum of maximum and minimum value of z is equal to:

The maximum value of the objective function $z = 10x + 15y$ of an L.P.P. subjected to the constraints

$2x + 4y \leq 8$,

$3x + y \leq 6$,

$-x - y \geq -4$,

$x \geq 0$, $y \geq 0$ is:

Consider the LPP: Minimize $z=-50x+20y$ subject to $2x-y\ge -5, 3x+y\ge 3, 2x-3y\le 12, x\ge 0, y\ge 0$. Then which of the following statements are TRUE?

(A) Corner points of the feasible region of the LPP are (0,5), (0,3), (1,0), (6,0).

(B) The optimum value of the objective function is -300

(C) Optimum value does not exist

(D) The optimum value of the objective function is 100

Choose the correct answer from the options given below: