For a linear programming problem, the maximum value of the objective function $z=2x+3y$ subject to constraints:

$x-y\le-1, -x+y\le0, x,y\ge0$ is

If the objective function $z = px + qy$ has its maximum value at the points (2, 1) and (0, 6), then the relationship between p and q is:

Which one of the following inequalities is redundant for the shaded feasible region (ABCDA) shown below?

If the corner points of the bounded feasible region for an LPP are $(5,0), (0,4), (0,2), (3,4)$, and $(0,7)$, then the minimum value of the objective function $z = 2x+5y$ occurs at :

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

If the corner points of the bounded feasible region of an LPP with objective function Maximize $z = 2x + 3y$ are (0,0), (1,2) and (1,1), then its optimal value is

For the objective function Z=-4x + 6y subject to the constraints 3x + 2y ≥ 5, 7x + 2y ≤ 9, x ≥ 0, y ≥ 0, the maximum value of Z occurs at $(a, b)$ and the minimum value of Z occurs at $(p, q)$ then the value of $\frac{a}{p} + \frac{b}{q}$ is: