The feasible region of the linear programming problem is represented below: <img src="https://balti.afterboards.in/2p1sfNGWOxx6GJZ" width="400px"/> The constraints of this LPP are

Let the corner points of the bounded feasible region of the linear programming problem (LPP) $Z = ax+by$ be: (0, 0), (2, 0), (20/19, 45/19) and (0, 3). If the optimal value of Z occurs at both points (2, 0) and (20/19, 45/19), then the relation between a and b is:

If the feasible region (shaded portion)of a LPP is as shown in the graph, then max $z = 50x + 15y$ is:

For LPP: Maximize $z = 2x + 3y$ subject to the constraints

$x + y \geq 2$, $x + 2y \geq 3$, $x \geq 0$, $y \geq 0$,

which of the following graph represents the feasible region of the above LPP as shaded portion?

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

The point/points which provides the optimal solution of the linear programming problem maximum $z = 3x+y$, $x+3y \le 12, 3x+y \le 12, x,y \ge 0$, is/are

If corner points of the bounded feasible region are (0, 0), (3, 0) and (0, 3) and objective function is $z = 4x + 7y$, then the maximum value of $z$ is