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

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

Consider an LPP:

Maximise $Z = 15x + 10y$

Subject to $2x + y \le 40$

$2x + 3y \le 80$

$x, y \ge 0$

Which of the following are correct?

A. The feasible region is bounded.

B. The corner points of the feasible region are $(0,0), (40,0), (10,20)$ and $(0,40)$.

C. The corner points of the feasible region are $(0,0), (20,0), (10,20)$ and $\left(0, \dfrac{80}{3}\right)$.

D. The maximum value of Z is 350.

Choose the correct answer from the options given below:

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

Consider the LPP: Minimize $Z = x + 2y$ subject to $2x + y \geq 3$, $x + 2y \geq 6$, $x, y \geq 0$. The optimal feasible solution occurs at

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: