The difference between the maximum and minimum values of the objective function $Z = 3x + 5y$, subject to the constraints $x + 3y \leq 60$, $x + y \geq 10$, $x - y \leq 0$, and $x, y \geq 0$ is

The shaded part of the given figure indicates the feasible region. Then the constraints are

Corner points of the feasible region for an $\operatorname{LPP}$ are $(0,2), (3,0), (6,0), (6,8)$ and $(0,5)$. Let $F = 4x + 6y$ be the objective function. The minimum value of $F$ occurs at $....$

The production of item $A$ is $x$ and the production of item $B$ is $y$. If the corner points of the bounded feasible region are $(1,0), (2,0), (0,2)$ and $(0,1)$,then the maximum profit $z = 2000x + 5000y$ is $\ldots \ldots$

The shaded area in the given figure is a solution set for some system of inequalities. The maximum value of the function $z=4x+3y$ subject to linear constraints given by the system is

$A$ fruit grower can use two types of fertilizer in his garden,brand $P$ and brand $Q$. The amounts (in $kg$) of nitrogen,phosphoric acid,potash,and chlorine in a bag of each brand are given in the table. Tests indicate that the garden needs at least $240 \, kg$ of phosphoric acid,at least $270 \, kg$ of potash,and at most $310 \, kg$ of chlorine.
If the grower wants to maximize the amount of nitrogen added to the garden,how many bags of each brand should be added? What is the maximum amount of nitrogen added?

	Brand $P$ ($kg$ per bag)	Brand $Q$ ($kg$ per bag)
Nitrogen	$3$	$3.5$
Phosphoric acid	$1$	$2$
Potash	$3$	$1.5$
Chlorine	$1.5$	$2$