The linear constraints, for which the shaded area in the figure is the feasible region of an LPP, are :

Which of the following statements are correct about the linear programming problem (LPP)?

A. Every point in the feasible region is a feasible solution of the given LPP.

B. An optimal solution of an LPP, if it exists, occurs at one of the extreme points of the convex set of the feasible solutions.

C. The feasible region for an LPP is always a convex set.

D. If an LPP admits two optimal solutions, it has an infinite number of optimal solutions.

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The linear inequalities satisfying the shaded feasible region given in the figure are

(A) $x \geq 0$, $y \geq 0$, $2x + y \geq 2$

(B) $x \geq 0$, $y \geq 0$, $2x + y \leq 2$

(C) $x \geq 0$, $y \geq 0$, $2x + y \geq 2$, $x + 2y \leq 8$, $x - y \leq 1$

(D) $x + 2y \geq 8$, $x - y \geq 1$

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A LPP $max\,z = ax+by$ having bounded feasible region with vertices on $(2,1), (3,2), (5,6)$ and $(1,7)$. Then which of following are TRUE?

A. $max\,z$ occurs at $(1,7)$ and $(5,6)$ if $b = 4a$

B. $max\,z$ occurs at $(1,7)$ and $(5,6)$ if $b = -4a$

C. $max\,z$ does not exist

D. if $max\,z$ occurs at $(1,7)$ and $(5,6)$, then $max\,z$ occurs for infinite number of value of $x$ and $y$

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Consider a LPP:

Maximize $Z=22x+18y$

Subject to:

$x+y\le 20$,

$360x+240y\le 5760$,

$x,y\ge 0$.

Which of the following statements are correct ?

A. The maximum value of $Z$ occurs at (0, 20).

B. The maximum value of $Z$ occurs at (8, 12).

C. The maximum value of $Z$ is 352.

D. The maximum value of $Z$ is 392.

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The point/points which provides the optimal solution of the linear programming problem maximum $z = 3x+y$, $x+3y \le 12, 3x+y \le 12, x,y \ge 0$, is/are

For a LPP, maximize $z=2x+3y$, subjected to constraints:

$x\ge2, x\le7, y\le x, x+y\le10, x\ge0, y\ge0$

Which of the following statements are TRUE ?

(A) Vertices of feasible region are (2, 0), (7, 0), (7, 3), (5, 5) and (2, 2).

(B) Maximum $z=25$ at point (5, 5).

(C) Maximum $z=25$ at infinite numbers of points.

(D) The feasible region is unbounded.

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