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 minimum value of $z = 3x + 2y$ subjected to the constraints $2x + y \geq 7, x + 2y \geq 8, x, y \geq 0$ is

Consider the following L.P.P

Max. z = 5x + 2y; subject to -2x - 3y ≤ -6, x - 2y ≤ 2, 3x + 2y ≤ 12, -3x + 2y ≤ 3 and x, y ≥ 0 then

The linear inequalities satisfying the shaded feasible region given in the figure are

(A) $x \geq 0$, $y \geq 0$, $2x + y \geq 2$

(B) $x \geq 0$, $y \geq 0$, $2x + y \leq 2$

(C) $x \geq 0$, $y \geq 0$, $2x + y \geq 2$, $x + 2y \leq 8$, $x - y \leq 1$

(D) $x + 2y \geq 8$, $x - y \geq 1$

Choose the correct answer from the options given below:

In reference to linear programming problem (LPP), which of the following statement is NOT correct?

The corner points of the bounded feasible region determined by the system of linear constraints are $(0,8)$, $(4,4)$, $(12,12)$, $(0,20)$. Let $z = px + qy$, where $p, q > 0$. Condition on $p$ and $q$ so that the maximum of $z$ occurs at both the points $(12,12)$, $(0,20)$ is

The point at which the maximum value of the function $Z=x+y$, subject to the constraints $x+2y\leq70$, $2x+y\leq95$, $x,y\geq0$, is obtained, is: