For the LPP,

$Z=20x+10y$

Subject to

$x+2y\le 40$

$3x+y\ge 30$

$4x+3y\ge 60$

$x,y\ge 0$

Match List-I with List-II

List-I	List-II
(A) $Max.Z$	(I) 180
(B) $Min.Z$	(II) 320
(C) $Max.Z - 2\,Min.Z$	(III) 240
(D) If $Min.Z$ is attained at $(\alpha,\beta)$, then $\alpha^2+\beta^2$ is	(IV) 800

Choose the correct answer from the options given below:

The corner points of the bounded feasible region of a linear programming problem are A(15,0), B(40,0), C(4, 18), D(6, 12) and objective function is $z = 20x+10y$, then which of the following are TRUE?

(A) Value of z at point A(15, 0) = 300.

(B) Value of z at point B(40, 0) = 800.

(C) Value of z at point C(4, 18) = 340.

(D) Maximum value of z = 800.

Choose the correct answer from the options given below:

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 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 the linear programming problem maximize $Z = 4x+3y$ subject to the constraints $x+y \ge 8$, $3x+5y \le 15$, $x\ge0, y\ge0$, the feasible region has

The corner points of a bounded feasible region are $A(15,0), B(40,0), C(4,18)$ and $D(6,12)$. If the objective function is $z = 20x + 10y$, then the difference in maximum and minimum value of $z$ is

For the linear programming problem:

Minimize $z = 2x - 5y$, subject to the constraints:

$x + 2y \ge 10$;

$3x + 4y \le 24$;

$x,y \ge 0$, then optimal value of $z$ is