The feasible region and optimal solution of a LPP with objective function, max.$(z) = 600x + 400y$, subject to :

$x + 2y \leq 12$, $2x + y \leq 12$, $x + 1.25y \geq 5$, $x \geq 0$ and $y \geq 0$, is:

The feasible region and optimal solution is _____

The corner points of the bounded feasible region for an LPP are (0,4), (4,4), (6,6), (0,12). If the objective function is $Z = px + qy, p > 0, q > 0$, then the condition on p and q so that maximum of Z occurs at (6,6) and (0,12) 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:

If corner points of the bounded feasible region of a linear programming problem are as in the figure given below and $z = px + qy$, $(p,q > 0)$ is an objective function. Then the relation between $p$ and $q$, when $z$ is maximum at $D(4,10)$ and $C(6,8)$, is:

An objective function $z = ax + by$ is maximum at points (15,15) and (0, 20). If $a, b \geq 0$ and $ab = 27$, then the maximum value of the objective function is

Consider the following L.P.P.

Minimize z = 400x + 300y subject to 100x + 200y ≥ 12000, 300x + 400y ≥ 20000, 200x + 100y ≥ 15000 and x, y ≥ 0. Then

For the LPP

Maximise $z = x + y$

subject to $x - y \leq -1$, $-x + y \leq 2$, $x, y \geq 0$, $z$ has :