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The feasible region for a LPP is shown in the given figure. The maximum value of $z = 2x + 5y$ is :

A LPP $max\,Z = 3x + 8y$ subjected to the constraints $2x + y \le 10$, $x + 3y \le 15$, $x,y \ge 0$, then $max\,Z$ is

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 $y$

Choose the correct answer from the options given below:

If the corner points of the bounded feasible region for an LPP are $(5,0), (0,4), (0,2), (3,4)$, and $(0,7)$, then the minimum value of the objective function $z = 2x+5y$ occurs at :

Consider a LPP given by:

Maximize $z = 3x+4y$,

Subject to: $x+y \le 40$, $x+2y \le 60$, $x,y \ge 0$.

Then which of the following statements are correct ?

A. The corner points of the feasible region are $(0,0), (0,30), (40,0), (20,20)$.

B. The feasible region is unbounded.

C. The feasible region is bounded.

D. The maximum value of $z=3x+4y$ is obtained at $(60,40)$.

Choose the correct answer from the options given below:

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

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:

Consider the linear programming problem (LPP):

Max Z= 4x + 3y

subject to the constraints:

$x\le 8, y\le 4, x\ge 0, y\ge 0$. At what coordinates will the objective function have optimal solution?

If the objective function for a LPP is $Z=3x+5y$ and the corner points of the bounded feasible region are (0, 0), (6, 0), (3, 5) and (0, 3), then the value of $|max(Z) - min(Z)|$ is:

The corner points of the bounded feasible region determined by the system of linear constraints of an LPP are (0, 0), (0, 8), (5, 0) and (4, 10). Let $z = 3x - 4y$ be the objective function, then the minimum value of $z$ is:

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:

For a LPP, the objective function is $z=4x+3y$ and the feasible region determined by a set of linear constraints is shown in the graph as a shaded portion. Which one of the following statement is true ?

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 point at which the maximum value of the function $Z=x+y$, subject to the constraints $x+2y\leq70$, $2x+y\leq95$, $x,y\geq0$, is obtained, is:

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

The number of feasible solutions of the linear programming problem as

Maximum $z=15x+30y$ subject to the constraints

$3x+y \leq 12$

$x+2y \leq 10$

$x \geq 0, y \geq 0$

is

For linear programming problem maximize $z=2x+3y$

Subject to the constraints $x+y \leq 4$

$x \leq 2$

$x \geq 0, y \geq 0$

Maximum value of z is

The maximum value of $z=5x+3y$ subjected to the constraints $2x+3y \ge 60, 2x+y \le 40; x,y \ge 0$ is:

The feasible region determined by the following constraints of a LPP

$x+y \ge 5$

$y \le 8$

$x \ge 0, y \ge 0$ is

Let the corner points of the bounded feasible region of an LPP determined by a set of constraints are A(1, 5), B(3, 2) and C(2, 1). If the objective function $z=2ax+by$, $a,b>0$ has maximum values at points A and B, and z has minimum value 8 at point C, then the value of $4a+b$ is:

The corner points of the bounded feasible region for an LPP are (0, 0), (6, 0), (4, 3) and (0, 8). The objective function $Z=px+qy$, $p,q>0$ has maximum value 360 at points (6, 0) and (4, 3). The value of $Z$ at (0, 8) is :

If the objective function for an LPP is $Z=4x+5y$ and the corner points for bounded feasible region are (10, 0), (5, 3), (2, 5) and (0, 6), then the minimum value of $Z$ occurs at

If the feasible region (shaded portion)of a LPP is as shown in the graph, then max $z = 50x + 15y$ is:

Which one of the region I, II, III, IV is represented by the constraints

$x + 3y \le 60, x + y \ge 10, x \le y, x \ge 0, y \ge 0$

For any linear programming problem the feasible region is shaded region as given below, then constraints are:

Consider an LPP:

Maximize $Z = 5x + y$

Subject to $x + 3y \le 12$

$3x + y \le 12$

and $x,y \ge 0$

then which of the following statements are TRUE ?

A. The corner points of the bounded feasible region are (0,0), (4,0), (3,3) and (0,4).

B. Maximum value of $z$ occurs at (3,3).

C. Maximum value of $z$ occurs at (4,0).

D. The maximum value of $z$ is 20.

Choose the correct answer from the options given below:

If the objective function for an LPP is $Z = 2x + 5y$ and the corner points of the bounded feasible region are (0, 0), (5, 0) , $\left(\dfrac{8}{5},\dfrac{6}{5}\right)$ and (0, 2) then the maximum value of $z$ occurs at

For a two variables linear programming problem (LPP), which of the following statement is correct ?

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

Which of the following group of constraints represents the feasible region given as shaded area below ?