If the objective function for an L.P.P. is $z = 3x + 4y$ and the corner points for unbounded feasible region are (9, 0), (4, 3), (2, 5) and (0, 8), then the minimum value of $z$ occurs at :

Objective function of a LPP represent

The minimum value of $z = 3x + 6y$ subject to the constraints $2x + 3y \leq 180$, $x + y \geq 60$, $x \geq 3y$, $x \geq 0$, $y \geq 0$ is :

The bounded feasible region of an LPP is shown in the diagram given below.

The objective function $z=3x+10y$ attains optimum values at :

A. Point (0,0)

B. Point (0,4)

C. Point (6,3)

D. Point (5,6)

Choose the correct answer from the options given below:

Match List I with List II

Choose the correct answer from the options given below:

If objective function $Z = 20x + 30y$ of an LPP is subject to the constraints $3x + 4y \geq 12$, $4x + y \geq 4$, $x \geq 0, y \geq 0$, then Z has :

(A) Min at (0, 4)

(B) Max at (0, 4)

(C) Min at (4, 0)

(D) Max at (4, 0)

(E) Min at $\left(\frac{4}{13}, \frac{36}{13}\right)$

Choose the correct answer from the options given below :

Corner points of the feasible region for an LPP are : (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5). Let $z = 4x + 6y$ be the objective function. Then, Max z $-$ Min z is equal to :