If the objective function $Z = px + qy$ ($p, q > 0$) of an LPP has minimum value 7p, at the corner points (2, 3) and (7, 0), then

The feasible reason for the constraints $x \geq 0$, $x + y \leq 1$ and $x - y \leq 1$, is situated in :

(A) I and II quadrant only

(B) I Quadrant

(C) II and IV Quadrant

(D) IV Quadrant

(E) I , II , III and IV Quadrant

Choose the correct answer from the option given below :

The minimum value of $Z = 30x + 10y$ subject to the constraints $x + 2y \leq 30, 3x + y \geq 30, 4x + 3y \geq 60, x, y \geq 0$ is

If the objective function for an L.P.P. is $z = 3x + 4y$ and the corner points for unbounded feasible region are (9, 0), (4, 3), (2, 5) and (0, 8), then the minimum value of $z$ occurs at :

For the feasible reason of a LPP as shown, if the equation of OA and BC are $y - 2x = 0$ and $y - 2x = 4$ respectively than constraints for LPP are

Match List I with List II

Choose the correct answer from the options given below:

The corner point of the feasible region determined by a set of linear constraints are : (0,0) , (0,4), (2,5) , (6,3) and (6,0) then which of the following point lie in the feasible region ?