The corner points O, A, B, C, D and E of the bounded feasible region determined by the system of linear constraints are shown in the given figure.

If $z = 3x - 4y$ be the objective function, then the minimum of z, is:

For any linear programming problem the feasible region is shaded region as given below, then constraints are:

The feasible region for a LPP is shown in the given figure. The maximum value of $z = 2x + 5y$ is :

If the corner points of the bounded feasible region of an LPP are (0,2), (3,0), (6,0), (6,8) and (0,5), then the minimum value of objective function F = 4x + 6y occurs at

For linear programming problem maximize $z=2x+3y$

Subject to the constraints $x+y \leq 4$

$x \leq 2$

$x \geq 0, y \geq 0$

Maximum value of z is

A manufacturing company makes two models M$_1$ and M$_2$ of a product. Each piece of M$_1$ requires 9 labour hours for fabricating and one labour hour for finishing. Each piece of M$_2$ require 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing, the maximum labour hours available are 180 and 30 respectively. The company makes a profit of Rs.800 on each piece of M$_1$ and Rs.1200 on each piece of M$_2$

The maximum profit will be at the point

The corner points of the feasible region determined by inequalities of LPP are $(4, 10)$, $(6, 8)$ and $(6, 5)$. Let $z = 3x + 4y$ be the objective function. Then the sum of maximum value of z and minimum value of z is :