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While solving an LPP, the corner points of a bounded feasible region were found to be (0,0), (1, 9), (3, 7), (4, 5.5) and (10, 0). The objective function $Z = 4x + y$ will maximise at:

The shaded unbounded area of an LPP is the result of constraints:

Given the following L.P.P., in which objective function represents the maximum profit ($Z$) (in Rs.) such as

Max. $Z=40x+30y$, subject to constraints:

$x+3y \le 12,\ 3x+y \le 12,\ x,y \ge 0$

The value of the maximum profit is:

The feasible region of an LPP is a bounded region by vertices (4, 18), (6, 12), (40, 0) and (15, 0). Then the point (15, 15) lies in the

A. open half plane of $x+2y<40$.

B. closed half plane of $3x+y\ge 30$.

C. closed half plane of $4x+3y\ge 60$.

D. feasible region of the given LPP.

Choose the correct answer from the options given below:

If a, b, c > 0 and $ax+by>c$, then its graph represents:

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:

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.

Choose the correct answer from the options given below:

If corner points of the bounded feasible region of a linear programming problem are as in the figure given below and $z = px + qy$, $(p,q > 0)$ is an objective function. Then the relation between $p$ and $q$, when $z$ is maximum at $D(4,10)$ and $C(6,8)$, is:

The corner points of the bounded feasible region determined by $2x+y \leq 10$, $x+3y \leq 15$, $x,y \geq 0$ are (0, 0), (5, 0), (3, 4) and (0, 5). Let $z = px+qy$, $p,q > 0$, then the relation between $p$ and $q$ so that the maximum of $z$ occurs at both (3, 4) and (0, 5), is

If the corner points of the bounded feasible region of a Linear Programming Problem are (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5), then the minimum value of the objective function $z = 2x+3y$ occurs at

The corner points of the bounded feasible region for an L.P.P are (0, 10), (5, 5), (15,15), and (0, 20). If the objective function is $Z=px+qy, p,q>0$, then the condition on $p$ and $q$ so that the maximum of $Z$ occurs at (15, 15) and (0, 20) is

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 number of corner points of the feasible region of an LPP determined by the constraints $x - y \geq 0$, $2y \leq x + 2, x \geq 0, y \geq 0$ is

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 graph of a linear programming problem(LPP) given below. If $\min z = 3x+5y$ is the objective function and shaded portion in the figure is the feasible region of the LPP, then constraints other than $x, y \geq 0$ are

The maximum value of $Z = 3x+2y$ subject to the constraints $x+2y \geq 8$, $x+y \leq 10, x \geq 0, y \geq 0$ is

Corner points of the bounded feasible region determined by the system of linear constraints are (0, 3), (1, 1), and (3, 0). Let $Z = px+qy$, where $p,q>0$. Condition on $p$ and $q$ so that the minimum of Z occurs at (3, 0) and (1, 1) is

The feasible region for a linear programming problem is shown in the figure.

Let $Z = 3x - 4y$ be the objective function, then minimum of Z occurs at the point

For a linear programming problem, the maximum value of the objective function $z=2x+3y$ subject to constraints:

$x-y\le-1, -x+y\le0, x,y\ge0$ is

In a linear programming problem, the corner points of the feasible region, determined by the system of linear inequalities are (0, 0), (5, 0), (3, 4) and (0, 5). Let $z=5x+qy, q>0$ be the objective function. For what value of q the maximum value of z occurs at both (3, 4) and (0, 5)?

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 feasible region for an LPP is shown in the given figure. Let $Z=3x+4y$ be the objective function. Then which of the following is/are TRUE?

(A) The minimum value of Z is 156

(B) The minimum value of Z is 152

(C) The maximum value of Z is 196

(D) Neither minimum nor maximum value of Z exists

Choose the correct answer from the options given below:

The linear constraints for which the shaded region in the figure are:

Let $Z=ux+vy$, $u,v>0$ be the objective function of a linear programming problem. Then the condition on $u$ and $v$ so that the maximum of $Z$ occurs at both points $(3,4)$ and $(0,5)$ is :

The feasible region for an L.P.P is always a/an

Which of the following terms are associated with a linear programming problem?

(A) Constraints

(B) Independent events

(C) Feasible region

(D) Objective function

Choose the correct answer from the options given below:

If $z = 3x + 4y$ be the objective function of a of a linear programming problem (LPP) and (3, 1), (2, 4), (0, 4), (5, 0) be corner points of the bounded feasible region. Then the maximum value of objective function is

The region represented by the system of inequalities $x, y \geq 0, y \leq 6, x + y \leq 3$

The corner points of the feasible region of a LPP with the constraints $x + 2y \leq 40$, $3x + y \geq 30$, $4x + 3y \geq 60$, $x, y \geq 0$ are

The corner points of the bounded feasible region determined by the system of linear constraints are $(0,8)$, $(4,4)$, $(12,12)$, $(0,20)$. Let $z = px + qy$, where $p, q > 0$. Condition on $p$ and $q$ so that the maximum of $z$ occurs at both the points $(12,12)$, $(0,20)$ is