The feasible region of an LPP is a bounded region by vertices (4, 18), (6, 12), (40, 0) and (15, 0). Then the point (15, 15) lies in the

A. open half plane of $x+2y<40$.

B. closed half plane of $3x+y\ge 30$.

C. closed half plane of $4x+3y\ge 60$.

D. feasible region of the given LPP.

Choose the correct answer from the options given below:

If $5x + y \leq 100$, $x + y \leq 60$, $x \geq 0$, $y \geq 0$. Then one of the corner points of the feasible region is :

The optimal value of linear programming problem maximum $Z = 3x + 4y$, subject to,

$x + 3y \leq 12$

$x + y \geq 8$

$x, y \geq 0$ is

Refer to the LPP given by $Z = 2.5x + y$, subject to constraints

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

In the given figure, If $Z_A$ = value of Z at A, $Z_C$ = value of Z at C and Max.(Z) = maximum value of Z, then which of the following relations between $Z_A$, $Z_C$ and Max.(Z) are correct?

A. $2Z_A = 5$ Max.(Z)

B. $5Z_A = 2Z_C$

C. $Z_A = 6 + Z_C$

D. $6+Z_A = Z_C$

Choose the correct answer from the options given below:

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:

The shaded unbounded area of an LPP is the result of constraints:

The corner points of the bounded feasible region determined by the system of linear constraints are $(0,8)$, $(4,4)$, $(12,12)$, $(0,20)$. Let $z = px + qy$, where $p, q > 0$. Condition on $p$ and $q$ so that the maximum of $z$ occurs at both the points $(12,12)$, $(0,20)$ is