Consider the LPP: Minimize $z=-50x+20y$ subject to $2x-y\ge -5, 3x+y\ge 3, 2x-3y\le 12, x\ge 0, y\ge 0$. Then which of the following statements are TRUE?

(A) Corner points of the feasible region of the LPP are (0,5), (0,3), (1,0), (6,0).

(B) The optimum value of the objective function is -300

(C) Optimum value does not exist

(D) The optimum value of the objective function is 100

Choose the correct answer from the options given below:

Given the following L.P.P., in which objective function represents the maximum profit ($Z$) (in Rs.) such as

Max. $Z=40x+30y$, subject to constraints:

$x+3y \le 12,\ 3x+y \le 12,\ x,y \ge 0$

The value of the maximum profit is:

If the objective function $Z = px + qy, p > 0, q > 0$ of a linear programming problem attains its optimal value at the points (4, 7) and (5, 5) and $pq = 50$ then

Which one of the region I, II, III, IV is represented by the constraints

$x + 3y \le 60, x + y \ge 10, x \le y, x \ge 0, y \ge 0$

The programming problem

Max $Z = 2x + 3y$ subject to the conditions $0 \leq x \leq 3, 0 \leq y \leq 4$ is :

For the graph of a linear programming problem(LPP) given below. If $\min z = 3x+5y$ is the objective function and shaded portion in the figure is the feasible region of the LPP, then constraints other than $x, y \geq 0$ are

The feasible region represented by the constraints: $x + 2y \geq 100$, $2x - y \leq 0$, $2x + y \leq 200$, $x \geq 0$, $y \geq 0$ of an LPP is: