Match List-I with List-II

List-I	List-II
(A) Corner point of a feasible region	(I) The line segment joining any two arbitrary points of the region always lies entirely within the region
(B) Bounded feasible region	(II) can not be enclosed within a circle
(C) Unbounded feasible region	(III) can be enclosed within a circle
(D) Convex region	(IV) Is a point of intersection of two boundary lines in the feasible region

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The feasible region corresponding to the linear constraints of a Linear Programming Problem (LPP) is represented by the shaded region in the given figure. Which of the following is not a constraint to the given LPP?

If the objective function for an L.P.P is $Z=2x+5y$ and the corner points for bounded feasible region are (8, 0), (2, 3), (3, 5), and (0, 7), then the minimum value of $Z$ occurs at

The maximum value of the objective function $z = 2x + 3y$ of an L.P.P. subjected to the constraints $x - y \le 1$, $x + y \le 3$, $x, y \ge 0$ is

For the linear programing problem,

$Minimize(Z) = 60x + 30y$

subject to: $2x - y \geq -5; 3x + y \geq 3; 2x - 3y \leq 12; x, y \geq 0$

the optimal value of $z$ is

Let the corner points of the bounded feasible region of the linear programming problem (LPP) $Z = ax+by$ be: (0, 0), (2, 0), (20/19, 45/19) and (0, 3). If the optimal value of Z occurs at both points (2, 0) and (20/19, 45/19), then the relation between a and b is:

In a LPP, let R be the feasible region.

A. If R is unbounded then a max./min. value of objective function may not exist.

B. If R is bounded then a max. and min. value of objective function will always exist.

C. If a solution exists, it must occur at a corner point.

D. If R is bounded then max. will exist but min. may or may not exist for an objective function.

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