If the objective function for an L.P.P is $Z=2x+5y$ and the corner points for bounded feasible region are (8, 0), (2, 3), (3, 5), and (0, 7), then the minimum value of $Z$ occurs at

With respect to the following shaded feasible region (ABCDEFA), the maximum value of the objective function z = 3x + 4y – 2 is at point(s):

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

For a LPP, maximize $z=2x+3y$, subjected to constraints:

$x\ge2, x\le7, y\le x, x+y\le10, x\ge0, y\ge0$

Which of the following statements are TRUE ?

(A) Vertices of feasible region are (2, 0), (7, 0), (7, 3), (5, 5) and (2, 2).

(B) Maximum $z=25$ at point (5, 5).

(C) Maximum $z=25$ at infinite numbers of points.

(D) The feasible region is unbounded.

Choose the correct answer from the options given below:

Consider a LPP with objective function $Z = px + qy$ subjected to certain constraints with a bounded feasible region such that maximum $Z = 80$ and minimum $Z = 52$, which occur at the corner points $(0, 8)$ and $(2, 4)$ respectively, Then the value of $p+q$ is:

For the given linear programming problem $z = ax + by; a, b > 0$ subject to the constraints $2x + y \leq 10, x + 3y \leq 15, x, y \geq 0$. If the corner points are (0,0), (5,0), (3,4) and (0,5) and z is maximum at both (3,4) and (0,5), then the relationship between a and b is

The corner points of the feasible region with the constraints $x + y \leq 30$, $x + y \geq 15$, $y \leq 20$, $x \leq 15$ and $x$, $y \geq 0$ are