Consider a LPP with objective function $z = ax + by$. If its feasible region R is bounded, then $z$

If the objective function $z = px + qy$ has its maximum value at the points (2, 1) and (0, 6), then the relationship between p and q is:

The maximum value of $z$ for the linear programing problem maximize $z = x + y$ subject to the constraints $x + 4y \leq 8, 2x + 3y \leq 12, 3x + y \leq 9, x \geq 0, y \geq 0$ is:

A manufacturing company makes two models M$_1$ and M$_2$ of a product. Each piece of M$_1$ requires 9 labour hours for fabricating and one labour hour for finishing. Each piece of M$_2$ require 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing, the maximum labour hours available are 180 and 30 respectively. The company makes a profit of Rs.800 on each piece of M$_1$ and Rs.1200 on each piece of M$_2$

The maximum profit will be at the point

The feasible region associated with the inequality $2x + 3y > 4$ is

If the objective function for an LPP is max.$(z) = 300x + 700y$ and the corner points for the bounded feasible region are $(6,0)$ $(5,0)$ $(0,6)$ $(4,4)$ and $(0,4)$, then the maximum values of z occurs at :

If the objective function for a LPP is $Z=3x+5y$ and the corner points of the bounded feasible region are (0, 0), (6, 0), (3, 5) and (0, 3), then the value of $|max(Z) - min(Z)|$ is: