The objective function for a L.P.P. is $Z = 5x + 7y$ and the corner points of the bounded feasible region are (0, 0), (7, 0), (3, 4) and (0, 2), then the maximum value of Z occurs at

In a LPP, Let R be the feasible region, then which of the following are TRUE?

A. If R is bounded, then the objective function Z has both a maximum and minimum value on R.

B. If R is unbounded, then the objective function Z may or may not have a maximum or minimum value.

C. If a optimal solution exists. It must occur at atleast one corner point of R.

D. If R is bounded, then maximum value will exist but minimum may or may not exist for an objective function Z.

Choose the correct answer from the options given 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:

The number of feasible solutions of the linear programming problem as

Maximum $z=15x+30y$ subject to the constraints

$3x+y \leq 12$

$x+2y \leq 10$

$x \geq 0, y \geq 0$

is

If the objective function for a LPP is $Z=3x+5y$ and the corner points of the bounded feasible region are (0, 0), (6, 0), (3, 5) and (0, 3), then the value of $|max(Z) - min(Z)|$ is:

If the corner points of the bounded feasible region for a Linear Programming Problem (LPP) are A(0,2), B(3, 0), C(2, 3) and D(3, 1), then the maximum value of the objective function $Z = 4x + 2y$ occurs at

Consider an LPP: Maximise $Z = 50x + 15y$ subjected to constraints

$x + y \leq 60$,

$5x + y \leq 100$,

$x, y \geq 0$.

If the maximum value of $Z$ occurs at $x = \alpha$ and $y = \beta$, then the value of $\alpha + \beta$ is