Which one of the following represents the correct feasible region determined by the following constraints of an LPP?

$x+y \geq 10,2 x+2 y \leq 25, x \geq 0, y \geq 0$

For the graph of a linear programming problem(LPP) given below. If $\min z = 3x+5y$ is the objective function and shaded portion in the figure is the feasible region of the LPP, then constraints other than $x, y \geq 0$ are

The minimum cost of the mixture is-

The corner points of the bounded feasible region determined by the system of linear constraints are (0, 0), (5, 0), (3, 4) and (0, 5). Let $Z = px + qy$ where $p, q > 0$. Condition on p and q so that the maximum of Z occurs at both (5, 0) and (3, 4) is

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 number of corner points of the feasible region determined by the constraints $2x - y \geq 0, x - 3y + 3 \geq 0, x \geq 0, y \geq 0$ is

The solution of LPP

max.(z) = $5x + 3y$ subject to

$2x + y \leq 6$

$x + y \leq 4$

$x \geq 0, y \geq 0$, is