The corner points of the bounded feasible region of an LPP are (0,0), (6,0), (4,3) and (0,6). Let $Z = ax + by$, where $a, b > 0$. Condition on $a$ and $b$ so that the maximum of $Z$ occurs at both (4, 3) and (0, 6) is

Max (z) = 5x + 10y subject to constraints:

$x + 2y < 120$

$x + y > 60$

$x - 2y > 0$

$x, y \geq 0$

Which of the following points do not lie in the feasible region of the above LPP ?

(A) (90, 15)

(B) (30, 15)

(C) (60, 20)

(D) (90, 10)

Choose the correct answer from the options given below:

In reference to a linear programming problem (LPP), which of the following statements are true?

A. The optimal value of the objective function is attained at the points given by intersections of inequation with the axes only.

B. The objective function of a LPP is a linear function to be optimized.

C. Every LPP admits an optimal solution.

D. The region represented by the inequation system, $x, y\geq0$, $x+2y\leq4, 3x+y\geq3, 4x+3y\geq6$ is bounded in the first quadrant.

Choose the correct answer from the options given below:

Which of the following is incorrect about the Linear Programming Problem (LPP)?

The number of corner points of the feasible region determined by the constraints $2x - y \geq 0, x - 3y + 3 \geq 0, x \geq 0, y \geq 0$ is

The feasible region of inequality $2x + 3y > 6$ is

If the objective function for a LPP is $Z=3x+4y$ and the corner points for bounded feasible region are (9,0), (4,3), (2,5) and (0,8), then the maximum value of Z occurs at