The point/points which provides the optimal solution of the linear programming problem maximum $z = 3x+y$, $x+3y \le 12, 3x+y \le 12, x,y \ge 0$, is/are

Which of the region shown in the given figures represents the feasible region bounded by the following constraints?

$4x + y \geq 80$, $2x + y \geq 60$, $x + y \leq 80$, $x \geq 0$, $y \geq 0$

The feasible region of inequality $2x + 3y > 6$ is

The corner points of the bounded feasible region determined by a set of constraints in an LPP are $P(0, 5)$, $Q(3, 5)$, $R(5, 0)$ and $S(4, 1)$. If the objective function is $z = ax + 2by$, where, $a, b > 0$, then the condition on $a$ and $b$ such that the maximum value of $z$ occurs at $Q$ and $S$ 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?

If $5x + y \leq 100$, $x + y \leq 60$, $x \geq 0$, $y \geq 0$. Then one of the corner points of the feasible region is :

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