Consider the linear programming problem :

Minimize $z = 50x + 70y$

Subject to $2x+y \geq 8$, $x+2y \geq 10$, $x \geq 0$, $y \geq 0$

The minimum value of objective function is :

Consider the following L.P.P minimize $z = x - 7y + 190$ subject to $x + y \le 8, x + y \ge 4, x \le 5, y \le 5$ and $x, y \ge 0$. Then which of the following is/are true?

(A) It's feasible region is unbounded

(B) It's feasible region is bounded

(C) It's feasible region has 5 corner points

(D) It's feasible region has 6 corner points

Choose the correct answer from the options given below:

Consider a LPP with objective function $z = ax + by$. If its feasible region R is bounded, then $z$

The objective function for a L.P.P. is $Z = 5x + 7y$ and the corner points of the bounded feasible region are (0, 0), (7, 0), (3, 4) and (0, 2), then the maximum value of Z occurs at

In a LPP, let R be the feasible region.

A. If R is unbounded then a max./min. value of objective function may not exist.

B. If R is bounded then a max. and min. value of objective function will always exist.

C. If a solution exists, it must occur at a corner point.

D. If R is bounded then max. will exist but min. may or may not exist for an objective function.

Choose the correct answer from the options given below:

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

The feasible region for a linear programming problem is shown in the figure.

Let $Z = 3x - 4y$ be the objective function, then minimum of Z occurs at the point