The solution of a LPP with basic feasible solutions (0, 0), (10, 0), (0, 20), (10, 15) and objective function Max $Z = 2x + 3y$ 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

In a linear programming problem, the corner points of the feasible region, determined by the system of linear inequalities are (0, 0), (5, 0), (3, 4) and (0, 5). Let $z=5x+qy, q>0$ be the objective function. For what value of q the maximum value of z occurs at both (3, 4) and (0, 5)?

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

Let $Z=ux+vy$, $u,v>0$ be the objective function of a linear programming problem. Then the condition on $u$ and $v$ so that the maximum of $Z$ occurs at both points $(3,4)$ and $(0,5)$ is :

The vertices of a closed convex polygon representing the feasible region of the LPP with, objective function $z = 5x + 3y$ are $(0, 0)$, $(3, 1)$, $(1, 3)$ and $(0, 2)$. The maximum value of $z$ 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: