Which one of the following set of constraints depicted the shaded region given below?

Consider the linear programming problem(LPP):

Minimize $Z = x + y$

$x + 2y \leq 4,$

$3x + y \geq 3,$

$4x + 3y \geq 6,$

$x, y \geq 0.$

Which of the following is correct for the above linear programming problem (LPP):

(A) The LPP has a bounded feasible region.

(B) The LPP has a unique optimal solution.

(C) The optimal value of the LPP exists at the point (3/2, 0)

(D) The corner points of the feasible region are (3/2, 0), (3/5, 6/5), (2/5, 6/5) and (4, 0)

Choose the correct answer from the options given below:

The feasible region represented by the constraints: $x + 2y \geq 100$, $2x - y \leq 0$, $2x + y \leq 200$, $x \geq 0$, $y \geq 0$ of an LPP is:

For the LPP,

$Z=20x+10y$

Subject to

$x+2y\le 40$

$3x+y\ge 30$

$4x+3y\ge 60$

$x,y\ge 0$

Match List-I with List-II

Choose the correct answer from the options given below:

The corner points of the bounded feasible region for an LPP are (0, 0), (6, 0), (4, 3) and (0, 8). The objective function $Z=px+qy$, $p,q>0$ has maximum value 360 at points (6, 0) and (4, 3). The value of $Z$ at (0, 8) is :

Which one of the following set of constraints represents the shaded region given below?

Consider the LPP: Maximize $z = 5x + 3y$ subject to $3x + 5y \leq 15$, $5x + 2y \leq 10$, $x,y \geq 0$. The optimal feasible solution occurs at