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

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)?

The corner points of the feasible region determined by a system of linear constraints are $(0, 0)$, $(0, 40)$, $(20, 40)$, $(60, 20)$, $(60, 0)$. If the objective function is $z = 4x + 3y$, then which one of the following is true?

The corner points of the bounded feasible region for an LPP are $(0,5), (6,6), (9,9)$ and $(0,12)$. 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 $(9,9)$ and $(0,12)$ is

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

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 maximum value of $z = 5x + 7y$ subjected to constraints $x + y \leq 5$, $x \geq 0$, $y \geq 0$ is: