While solving an LPP, the corner points of a bounded feasible region were found to be (0,0), (1, 9), (3, 7), (4, 5.5) and (10, 0). The objective function $Z = 4x + y$ will maximise at:

The corner points of the bounded feasible region for an LPP are (0, 20), (3,12), (6,8), and (0,15). The objective function is $Z = \alpha x + \beta y$, where $\alpha, \beta > 0$. If the maximum of Z occurs at the corner points (3,12) and (6,8), then the relationship between $\alpha$ and $\beta$ is:

The corner points of the bounded feasible region determined by a set of constraints (linear inequalities) are A(0, 5), B(3, 5), C(5, 0) and D(4, 1) and the objective function is z = $px$ + 2$qy$ where p,q > 0. The condition on $p$ and $q$ such that the maximum z occurs at B and D, is:

In a Linear Programming problem, the objective function is always :

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:

Consider an LPP: Maximise $Z = 50x + 15y$ subjected to constraints

$x + y \leq 60$,

$5x + y \leq 100$,

$x, y \geq 0$.

If the maximum value of $Z$ occurs at $x = \alpha$ and $y = \beta$, then the value of $\alpha + \beta$ is

Which one of the following set of constraints does the given shaded region represent?