The corner points of the bounded feasible region determined by the system of linear constraints are $(0, 0), (5, 0), (6, 5), (6, 8), (4, 10), (0,8)$. Let $z = 3x - 4y$ be the objective function. Then the minimum value of the objective function z occurs at

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:

The maximum value of the objective function $Z = 8x + 2y$ of an LPP subject to constraints $2x + y \leq 3, 2x + 3y \leq 6, x \geq 0, y \geq 0$ is:

Let $Z=ux+vy$, $u,v>0$ be the objective function of a linear programming problem. Then the condition on $u$ and $v$ so that the maximum of $Z$ occurs at both points $(3,4)$ and $(0,5)$ is :

Which one of the following set of constraints represents the shaded region given below?

The corner points of the bounded feasible region for an LLP are: (5, 5), (15, 15), (0, 20) and (0, 10). Let $z = 3x + 9y$ be the objective function. Then the value of $maximum(z) - minimum(z)$ 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: