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

For a linear programming problem, the feasible region is shown in the figure by shaded portion, then linear constraints are

The maximum value of $z = 4x + 2y$, subjected to the constraints:

$2x + 3y \le 18$, $x + y \ge 5$;

$x, y \ge 0$, is

Which one of the following inequalities is redundant for the shaded feasible region (ABCDA) shown below?

Which of the following statements are correct in reference to the linear programming problem(LPP):

Maximize ${Z} = 5x + 2y$

subject to the following constraints

$3x + 5y \leq 15$, $5x + 2y \leq 10$, $x \geq 0, y \geq 0$.

(A) The LPP has a unique optimal solution at $(2, 0)$ only.

(B) The feasible region is bounded with corner points $(0, 0)$, $(2, 0)$, $(20/19, 45/19)$ and $(0, 3)$.

(C) The optimal value is unique, but there are an infinite number of optimal solutions.

(D) The feasible region is unbounded.

Choose the correct answer from the options given below:

If $z = 3x + 4y$ be the objective function of a of a linear programming problem (LPP) and (3, 1), (2, 4), (0, 4), (5, 0) be corner points of the bounded feasible region. Then the maximum value of objective function is

Refer to the LPP given by $Z = 2.5x + y$, subject to constraints

$3x + y \le 12; 3y + x \le 12; x, y \ge 0$:

In the given figure, If $Z_A$ = value of Z at A, $Z_C$ = value of Z at C and Max.(Z) = maximum value of Z, then which of the following relations between $Z_A$, $Z_C$ and Max.(Z) are correct?

A. $2Z_A = 5$ Max.(Z)

B. $5Z_A = 2Z_C$

C. $Z_A = 6 + Z_C$

D. $6+Z_A = Z_C$

Choose the correct answer from the options given below: