Solution of the following $LP$ problem
Minimize $z = -3x + 2y$
subject to $0 \leq x \leq 4, 1 \leq y \leq 6, x + y \leq 5$ 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	$1.5$	$2$

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

For the following shaded area,the linear constraints except $x, y \geq 0$ are

The feasible region of the $L$.$P$.$P$. (Linear Programming Problem) to maximize $z = 70x + 50y$ subject to the constraints $8x + 5y \leq 60$,$4x + 5y \leq 40$ and $x \geq 0, y \geq 0$ is:

Find the maximum value of $z = 2x + 6y$ subject to the constraints $-x + y \leq 1$,$2x + y \leq 2$,$x \geq 0$,and $y \geq 0$.