The corner points of the feasible region are $A(3,3), B(20,3), C(20,10), D(18,12)$ and $E(12, 12)$. The maximum value of $Z=2x+3y$ is $.......$

The feasible region (shaded) for a $LPP$ is shown in the adjacent figure. Maximize $Z = 5x + 7y$.

Solve the Linear Programming Problem graphically:
Minimise $Z = 3x + 5y$
subject to the constraints:
$x + 3y \geq 3$
$x + y \geq 2$
$x, y \geq 0$

The corner points of the feasible region determined by the system of linear constraints are $(0, 10)$, $(5, 5)$, $(15, 15)$, and $(0, 20)$. Let $z = px + qy$ where $p, q > 0$. The condition on $p$ and $q$ such that the maximum value of $z$ occurs at both points $(15, 15)$ and $(0, 20)$ is

The objective function of a Linear Programming Problem $(L.P.P.)$ defined over a convex set attains its optimum value at

Determine the maximum value of $Z=3x+4y$ if the feasible region (shaded) for a $LPP$ is shown in the adjacent figure.