The corner points of the 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

The maximum value of the objective function $z = 10x + 15y$ of an L.P.P. subjected to the constraints

$2x + 4y \leq 8$,

$3x + y \leq 6$,

$-x - y \geq -4$,

$x \geq 0$, $y \geq 0$ is:

The feasible region and optimal solution of a LPP with objective function, max.$(z) = 600x + 400y$, subject to :

$x + 2y \leq 12$, $2x + y \leq 12$, $x + 1.25y \geq 5$, $x \geq 0$ and $y \geq 0$, is:

The feasible region and optimal solution is _____

The objective function (z) to maximize the profit is:

A Linear Programming Problem (LPP) consists of which of the following components?

(A) Decision variables

(B) The graphical compliment

(C) The objective function

(D) The linear constraints

Choose the correct answer from the options given below:

A LPP $max\,z = ax+by$ having bounded feasible region with vertices on $(2,1), (3,2), (5,6)$ and $(1,7)$. Then which of following are TRUE?

A. $max\,z$ occurs at $(1,7)$ and $(5,6)$ if $b = 4a$

B. $max\,z$ occurs at $(1,7)$ and $(5,6)$ if $b = -4a$

C. $max\,z$ does not exist

D. if $max\,z$ occurs at $(1,7)$ and $(5,6)$, then $max\,z$ occurs for infinite number of value of $x$ and $y$

Choose the correct answer from the options given below:

Let the corner points of the bounded feasible region of the linear programming problem (LPP) $Z = ax+by$ be: (0, 0), (2, 0), (20/19, 45/19) and (0, 3). If the optimal value of Z occurs at both points (2, 0) and (20/19, 45/19), then the relation between a and b is: