The corner points of the bounded feasible region for an LPP are (0,4), (4,4), (6,6), (0,12). If the objective function is $Z = px + qy, p > 0, q > 0$, then the condition on p and q so that maximum of Z occurs at (6,6) and (0,12) is

The corner points of the bounded feasible region determined by a set of constraints (linear inequalities) are A(0, 5), B(3, 5), C(5, 0) and D(4, 1) and the objective function is z = $px$ + 2$qy$ where p,q > 0. The condition on $p$ and $q$ such that the maximum z occurs at B and D, is:

The corner points of the bounded feasible region determined by the system of linear constraints are $(0, 0)$, $(5, 0)$, $(6, 5)$, $(6, 8)$, $(4, 10)$, $(0, 8)$. Let $Z = 3x - 4y$ be the objective function. The minimum value of Z occurs at

The maximum value of $Z = 3x+2y$ subject to the constraints $x+2y \geq 8$, $x+y \leq 10, x \geq 0, y \geq 0$ is

The programming problem

Max $Z = 2x + 3y$ subject to the conditions $0 \leq x \leq 3, 0 \leq y \leq 4$ is :

In reference to a linear programming problem (LPP), which of the following statements are true?

A. The optimal value of the objective function is attained at the points given by intersections of inequation with the axes only.

B. The objective function of a LPP is a linear function to be optimized.

C. Every LPP admits an optimal solution.

D. The region represented by the inequation system, $x, y\geq0$, $x+2y\leq4, 3x+y\geq3, 4x+3y\geq6$ is bounded in the first quadrant.

Choose the correct answer from the options given below:

The corner points of the bounded feasible region for an LPP are $(0,5), (6,6), (9,9)$ and $(0,12)$. 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 $(9,9)$ and $(0,12)$ is