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The point which provides the optimal solution of the linear programming problem

maximize $z = 21x + 35y$

$3x + 2y \leq 30$

$4x + 5y \leq 60$

$x \geq 0, y \geq 0$

has the coordinates

If the feasible region of an LPP is bounded and the corresponding objective function is $z = 5x - 9y$, then the objective function attains:

The corner points of a bounded feasible region are (0, 5), (6, 1), (17, 2) and (4, 29). If the maximum value of objective function $z = px + qy$ where $p$ and $q > 0$ occurs at two points (17, 2) and (4, 29), then the relation between $p$ and $q$ is:

The sum of the x-coordinates of the corner points of the feasible region for the LPP: Minimize $z = 3x + 2y$ subject to constraints $x + y \leq 14$, $x \geq 4$, $x \leq 8, y \geq 0$ is

The objective function of an LPP is $z = ax + \beta y, (a, \beta > 0)$ in that has to be maximized/minimized subject to constraints

$x + y \leq 2$, $x \geq 0$, $y \geq 0$. Then max (z) $-$ min (z) is equal to

As per the below-mentioned graph of shaded bounded feasible region of the LPP, the maximum value of the objective function $z = 2x + y$ is

A Linear Programming Problem (LPP) consists of which of the following components?

(A) Decision variables

(B) The graphical compliment

(C) The objective function

(D) The linear constraints

Choose the correct answer from the options given below:

Consider an LPP: Maximise $Z = 50x + 15y$ subjected to constraints

$x + y \leq 60$,

$5x + y \leq 100$,

$x, y \geq 0$.

If the maximum value of $Z$ occurs at $x = \alpha$ and $y = \beta$, then the value of $\alpha + \beta$ is

Linear inequalities corresponding to the shaded feasible region OABCO in the given figure are

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?

The corner points of the bounded feasible region for an LPP are: (5, 5), (15, 15), (0, 20) and (0, 10). Let $z = 3x + 9y$ be the objective function. Then the value of $maximum(z) - minimum(z)$ 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

The maximum value of $z$ for the linear programing problem maximize $z = x + y$ subject to the constraints $x + 4y \leq 8, 2x + 3y \leq 12, 3x + y \leq 9, x \geq 0, y \geq 0$ is:

For a linear programming problem, the feasible region is shown in the figure by shaded portion, then linear constraints are

For the L.P.P. Maximize z = 10x + 6y subjected to

3x + y ≤ 12,

2x + 5y ≤ 34,

x, y ≥ 0.

Then the feasible region represented by system of inequalities is

The corner points of the bounded feasible region determined by the system of linear constraints are (0, 10), (5, 5), (15, 15), (0, 20). Let z = px + qy where p, q > 0. Then the condition on p and q so that the maximum value of z occurs at (15, 15) and (0, 20) is

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

Choose the correct answer from the options given below:

In an LPP, the feasible region represented by the set off constraints $2x + 3y \leq 18$, $x + y \leq 10$, $x \geq 0$, $y \geq 0$ is

The corner points of the bounded feasible region for an LPP are (0,4), (4,4), (6,6), (0,12). If the objective function is $Z = px + qy, p > 0, q > 0$, then the condition on p and q so that maximum of Z occurs at (6,6) and (0,12) is

The solution set of the linear constraints $x - 2y \geq 0, 2x - y \leq -4, x \geq 0$ and $y \geq 0$ is

The corner points of the bounded feasible region associated with the LPP: Maximize $Z=px+qy$, $p,q>0$ are $(0, 0)$, $(3.5, 0)$, $\left(\frac{112}{59}, \frac{135}{59}\right)$ and $(0, 3)$. If the optimum value of Z occurs at both $\left(\frac{112}{59}, \frac{135}{59}\right)$ and $(0, 3)$, then

A person can sell a maximum of 20 units of shirts and pants on which a profit of ₹40 is made on each shirt and a profit of ₹30 on each pant. A minimum of 2 shirts are being sold, while pants are sold at least 4 times as many as shirts. Then the maximum profit is:

Which one of the following set of constraints represents the shaded region given below?

If the corner points of the bounded feasible region of an LPP are (0,2), (3,0), (6,0), (6,8) and (0,5), then the minimum value of objective function F = 4x + 6y occurs at

The corner points of the bounded feasible region for an LPP are (0, 20), (3,12), (6,8), and (0,15). The objective function is $Z = \alpha x + \beta y$, where $\alpha, \beta > 0$. If the maximum of Z occurs at the corner points (3,12) and (6,8), then the relationship between $\alpha$ and $\beta$ is:

The maximum value of a LPP $z = 3x + 4y$ subject to the constraints: $x + y \leq 6$, $x \geq 0$, $y \geq 0$ is:

If $z = 5x + 8y$ is the objective function of a LPP and (0, 0), (3, 1), (2, 4), (0, 3), (5, 0) are corner points of the bounded feasible region, then the maximum value of the objective function is

The corner points of the feasible region with the constraints $x + y \leq 30$, $x + y \geq 15$, $y \leq 20$, $x \leq 15$ and $x$, $y \geq 0$ are

The feasible region of a LPP is bounded. The corresponding objective function is Z= 6x - 7y. Then objective function attains:

The feasible region of a linear programming problem is bounded. The corresponding objective function is Z= 3x-4y. The objective function attains