The feasible region for a LPP is shown in the given figure. The maximum value of $z = 2x + 5y$ 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 maximum value of $z = 3x + 4y$ subject to the constraints

$x + y \geq 2, 2x + 3y \leq 6, x \geq 0, y \geq 0$ is

For the linear programming problem (LPP),

$Maximize Z = 7x + 9y$, subject to constraints,

$x - y \le -1, -x + y \le 0, x, y \ge 0.$

Which of the following is correct?

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:

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

The feasible region associated with the inequality $2x + 3y > 4$ is