If the objective function for an LPP is $Z=4x+5y$ and the corner points for bounded feasible region are (10, 0), (5, 3), (2, 5) and (0, 6), then the minimum value of $Z$ occurs at

The corner points of the bounded feasible region for an L.P.P are (0, 10), (5, 5), (15,15), and (0, 20). If the objective function is $Z=px+qy, p,q>0$, then the condition on $p$ and $q$ so that the maximum of $Z$ occurs at (15, 15) and (0, 20) is

If the optimal value of the objective function $z = px + y$ of an L.P.P occurs at two corner points (2, 11) and (4, 5) of its bounded feasible region, then its optimal value is

For the linear programming problem(LPP),

Maximize $Z = 4x + y$

$x + y \leq 5$

$3x + y \leq 9$

$x,y \geq 0$.

Which of the following are NOT true?

(A) The given LPP has unbounded feasible region.

(B) The corner points of the feasible region are (0,0), (0, 5), (3, 2) and (3, 0).

(C) The optimal value of the objective function is 12.

(D) The given LPP has a unique optimal solution.

Choose the correct answer from the options given below:

Which one of the following set of constraints represents the shaded region given below?

Consider the following L.L.P.

Minimize z = 30x - 30y + 1800;

subject to x + y ≤ 30, x ≤ 15, y ≤ 20, x + y ≥ 15 and x, y ≥ 0.

Then it attains its optimal value at the point

The corner points of the bounded feasible region for a linear programming problem (LPP) are (0, 3/2), (1, 2) and (4, 0). If the objective function is Z = ax + by, where 'a' and 'b' are positive, then the condition on 'a' and 'b' so that the maximum of Z occurs at (1, 2) and (4, 0) is: