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:

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:

The linear constraints for which the shaded region in the figure is the solution set, are

Which one of the region I, II, III, IV is represented by the constraints

$x + 3y \le 60, x + y \ge 10, x \le y, x \ge 0, y \ge 0$

The solution of LPP

max.(z) = $5x + 3y$ subject to

$2x + y \leq 6$

$x + y \leq 4$

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

The corner points of the feasible region determined by the system of linear constraints are (0, 0), (0, 40), (20, 40), (60, 20), (60, 0). The objective function is $z = 4x + 3y$.

Compare the quantity in Column - A and Column - B.

For the constriants $x + y \le 60$, $5x + y \le 100$ and $x \ge 0, y \ge 0$, the feasible region is: