For the L.P.P. Maximize z = 10x + 6y subjected to 3x + y ≤ 12, 2x + 5y ≤ 34, x, y ≥ 0. Then the feasible region represented by system of inequalities is

If the feasible region (shaded portion)of a LPP is as shown in the graph, then max $z = 50x + 15y$ is:

Which of the following group of constraints represents the feasible region given as shaded area below ?

Consider an LPP: Maximise $Z = 50x + 15y$ subjected to constraints

$x + y \leq 60$,

$5x + y \leq 100$,

$x, y \geq 0$.

If the maximum value of $Z$ occurs at $x = \alpha$ and $y = \beta$, then the value of $\alpha + \beta$ is

If the objective function for an LPP is $Z = 2x + 5y$ and the corner points of the bounded feasible region are (0, 0), (5, 0) , $\left(\dfrac{8}{5},\dfrac{6}{5}\right)$ and (0, 2) then the maximum value of $z$ occurs at

Owner of a whole sale computers shop plans to sell 2 types of computers. A desktop and portable model. If $x$ is the number of desktops and $y$ is the number of portable model and the shop's capacity cannot exceed 250 units. Which of the following is correct ?

The corner points of the bounded feasible region of an LPP are (0,0), (6,0), (4,3) and (0,6). Let $Z = ax + by$, where $a, b > 0$. Condition on $a$ and $b$ so that the maximum of $Z$ occurs at both (4, 3) and (0, 6) is