The optimal value of linear programming problem maximum $Z = 3x + 4y$, subject to,

$x + 3y \leq 12$

$x + y \geq 8$

$x, y \geq 0$ is

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

Consider an LPP:

Maximize $Z = 5x + y$

Subject to $x + 3y \le 12$

$3x + y \le 12$

and $x,y \ge 0$

then which of the following statements are TRUE ?

A. The corner points of the bounded feasible region are (0,0), (4,0), (3,3) and (0,4).

B. Maximum value of $z$ occurs at (3,3).

C. Maximum value of $z$ occurs at (4,0).

D. The maximum value of $z$ is 20.

Choose the correct answer from the options given below:

The corner points of the bounded feasible region determined by the system of linear inequalities are $(0, 0)$, $(2, 4)$, $(0, 5)$ and $(4, 0)$. If the maximum value of $z = ax + by$, where $a, b > 0$ occurs at both $(2, 4)$ and $(4, 0)$, then

If a, b, c > 0 and $ax+by>c$, then its graph represents:

The corner points of the bounded feasible region determined by the system of linear constraints are (0, 0), (0, 9), (2, 10), (6, 8), (10, 0). If the objective function is $Z=6x+5y$, then (Maximum value of $Z$ – Minimum value of $Z$) is equal to:

The constraints are -

A. $2x + y \leq 8$

B. $2x + y \geq 8$

C. $x + 2y \leq 10$

D. $x + 2y \geq 10$

E. $x, y \geq 0$

Choose the correct answer from the options given below: