Which of the following statements are correct about the linear programming problem (LPP)?

A. Every point in the feasible region is a feasible solution of the given LPP.

B. An optimal solution of an LPP, if it exists, occurs at one of the extreme points of the convex set of the feasible solutions.

C. The feasible region for an LPP is always a convex set.

D. If an LPP admits two optimal solutions, it has an infinite number of optimal solutions.

Choose the correct answer from the options given below:

With respect to the following shaded feasible region (ABCDEFA), the maximum value of the objective function z = 3x + 4y – 2 is at point(s):

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

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 associated with the LPP: Maximize $Z=px+qy$, $p,q>0$ are $(0, 0)$, $(3.5, 0)$, $\left(\frac{112}{59}, \frac{135}{59}\right)$ and $(0, 3)$. If the optimum value of Z occurs at both $\left(\frac{112}{59}, \frac{135}{59}\right)$ and $(0, 3)$, then

For the L.P.P. Maximize z = 10x + 6y subjected to

3x + y ≤ 12,

2x + 5y ≤ 34,

x, y ≥ 0.

Then the feasible region represented by system of inequalities is

If $5x + y \leq 100$, $x + y \leq 60$, $x \geq 0$, $y \geq 0$. Then one of the corner points of the feasible region is :