A region of a factory must be isolated, as employees are exposed to accident risks there. This region is represented by the gray portion (quadrilateral with area S) in the figure.
So that employees are informed about the location of the isolated area, informational posters will be posted throughout the factory. To create them, a programmer will use software that allows drawing this region from a set of algebraic inequalities.
The inequalities that should be used in the said software for drawing the isolation region are
(A) $3y - x \leq 0 ; 2y - x \geq 0 ; y \leq 8 ; x \leq 9$
(B) $3y - x \leq 0 ; 2y - x \geq 0 ; y \leq 9 ; x \leq 8$
(C) $3y - x \geq 0 ; 2y - x \leq 0 ; y \leq 9 ; x \leq 8$
(D) $4y - 9x \leq 0 ; 8y - 3x \geq 0 ; y \leq 8 ; x \leq 9$
(E) $4y - 9x \leq 0 ; 8y - 3x \geq 0 ; y \leq 9 ; x \leq 8$

5. Given that $\mathrm { x } , \mathrm { y }$ satisfy the constraints $\left\{ \begin{array} { c } x - y \geq 0 \\ x + y - 4 \leq 0 \\ y \geq 1 \end{array} \right.$, then the maximum value of $\mathrm { z } = - 2 \mathrm { x } + \mathrm { y }$ is
(A) $- 1$
(B) $- 2$
(C) $- 5$
(D) $1$

If the system of inequalities $\left\{ \begin{array} { c } x + y - 2 \leq 0 \\ x + 2 y - 2 \geq 0 \\ x - y + 2 m \geq 0 \end{array} \right.$ represents a triangular region with area equal to $\frac { 4 } { 3 }$, then the value of $m$ is
(A) $-3$
(B) $1$
(C) $\frac { 4 } { 3 }$
(D) $3$

5. If variables $x$ and $y$ satisfy the constraint conditions $\left\{ \begin{array} { l } x + 2 y \geq 0 , \\ x - y \leq 0 , \\ x - 2 y + 2 \geq 0 , \end{array} \right.$ then the minimum value of $z = 2 x - y$ equals
A. $- \frac { 5 } { 2 }$
B. $- 2$
C. $- \frac { 3 } { 2 }$
D. 2

14. If $x , y$ satisfy the constraint conditions $\left\{ \begin{array} { c } x + y - 5 \leq 0 \\ 2 x - y - 1 \geq 0 \\ x - 2 y + 1 \leq 0 \end{array} \right.$, then the maximum value of $z = 2 x + y$ is $\_\_\_\_$ .

If $\mathrm { x } , \mathrm { y }$ satisfy the constraint conditions $\left\{ \begin{array} { l } x - y + 1 \geqslant 0 , \\ x - 2 y \leqslant 0 , \\ x + 2 y - 2 \leqslant 0 , \end{array} \right.$ then the maximum value of $z = x + y$ is $\_\_\_\_$ .

2. Let variables $x , y$ satisfy the constraint conditions $x - 2y \geq 0$, $x \leq 2$, $y \geq 0$. Then the maximum value of the objective function $z = 3x + y$ is
(A) 7
(B) 8
(C) 9
(D) 14

Variables $x, y$ satisfy the constraints $\left\{\begin{array}{c}x + 2 \geq 0, \\ x - y + 3 \geq 0, \\ 2x + y - 3 \leq 0,\end{array}\right.$ then the maximum value of the objective function $Z = x + 6y$ is
(A) 3
(B) 4
(C) 18
(D) 40

Let $x, y$ satisfy the constraint conditions $\left\{ \begin{array}{l} x - y \geq 1 \\ y \geq 0 \end{array} \right.$. Then the maximum value of $z = x + y$ is
A. 0
B. 1
C. 2
D. 3

Let $x$ and $y$ satisfy the constraints $\left\{ \begin{array} { l } x + 2 y \leqslant 1, \\ 2 x + y \geqslant - 1, \\ x - y \leqslant 0, \end{array} \right.$ then the minimum value of $z = 3 x - 2 y$ is \_\_\_\_

Let $x, y$ satisfy the linear constraints $\left\{\begin{array}{l} 2x - 3y + 3 \geq 0, \\ y + 3 \geq 0, \\ 3x - 3 \leq 0 \end{array}\right.$ and let $z = 2x + y$. The minimum value of $z$ is
A. $-15$
B. $-9$
C. $1$
D. $9$

If $x , y$ satisfy the constraints $\left\{ \begin{array} { l } x - 2 y - 2 \leq 0 , \\ x - y + 1 \geq 0 , \\ y \leq 0 , \end{array} \right.$ then the maximum value of $z = 3 x + 2 y$ is \_\_\_\_

If $x , y$ satisfy the constraints $\left\{ \begin{array} { l } x - 2 y - 2 \leqslant 0 , \\ x - y + 1 \geqslant 0 , \\ y \leqslant 0 , \end{array} \right.$ then the maximum value of $z = 3 x + 2 y$ is $\_\_\_\_$

Given the constraints $\left\{ \begin{array} { l } x + 2 y - 5 \geq 0 , \\ x - 2 y + 3 \geq 0 , \\ x - 5 \leq 0 , \end{array} \right.$ the minimum value of $z = x + y$ is \_\_\_\_.

If $x , y$ satisfy the constraints $\left\{ \begin{array} { l } x + 2 y - 5 \geqslant 0 , \\ x - 2 y + 3 \geqslant 0 , \\ x - 5 \leqslant 0 , \end{array} \right.$ then the maximum value of $z = x + y$ is $\_\_\_\_$.

If $x , y$ satisfy $| x | \leqslant 1 - y$ and $y \geqslant - 1$, then the maximum value of $3 x + y$ is (A) $- 7$ (B) 1 (C) 5 (D) 7

13. If variables $x , y$ satisfy the constraint conditions $\left\{ \begin{array} { l } 2 x + 3 y - 6 \geq 0 , \\ x + y - 3 \leq 0 , \\ y - 2 \leq 0 , \end{array} \right.$ then the maximum value of $z = 3 x - y$ is $\_\_\_\_$ .

11. Let the plane region represented by the system of inequalities $\left\{ \begin{array} { l } x + y \geq 6 , \\ 2 x - y \geq 0 \end{array} \right.$ be $D$ . Proposition $p : \exists ( x , y ) \in D , 2 x + y \geq 9$ ; Proposition $q : \forall ( x , y ) \in D , 2 x + y \leq 12$ . Four propositions are given below:
(1) $p \vee q$
(2) $\neg p \vee q$
(3) $p \wedge \neg q$
(4) $\neg p \wedge \neg q$
The numbers of all true propositions among these four are
A. (1)(3)
B. (1)(2)
C. (2)(3)
D. (3)(4)

If $x , y$ satisfy the constraint conditions $\left\{ \begin{array} { l } 2 x + y - 2 \leqslant 0 , \\ x - y - 1 \geqslant 0 , \\ y + 1 \geqslant 0 , \end{array} \right.$ then the maximum value of $z = x + 7 y$ is $\_\_\_\_$

If $x , y$ satisfy the constraints $\left\{ \begin{array} { l } x + y \geqslant 0 , \\ 2 x - y \geqslant 0 , \\ x \leqslant 1 , \end{array} \right.$ then the maximum value of $z = 3 x + 2 y$ is $\_\_\_\_$ .

If $x , y$ satisfy the constraints $\left\{ \begin{array} { l } x + y \geqslant 0 , \\ 2 x - y \geqslant 0 , \\ x \leqslant 1 , \end{array} \right.$ then the maximum value of $z = 3 x + 2 y$ is $\_\_\_\_$ .

Given $\left\{ \begin{array} { l } x + y \geq 2 \\ y \geq 0 \\ x + 2 y - 3 \leq 0 \end{array} \right.$, find the maximum value of $z = y - 2 x$ as $\_\_\_\_$

If $x , y$ satisfy the constraints $\left\{ \begin{array} { l } x + y \geqslant 2 , \\ x + 2 y \leqslant 4 , \end{array} \right.$ then the maximum value of $z = 2 x - y$ is
A. $- 2$
B. 4
C. 8
D. 12

Let $x , y$ satisfy the constraints $\left\{ \begin{array}{l} -2x + 3y \leqslant 3 \\ 3x - 2y \leqslant 3 \\ x + y = 1 \end{array} \right.$ . Let $z = 3x + 2y$ . The maximum value of $z$ is $\_\_\_\_$ .

If $x , y$ satisfy the constraints $\left\{ \begin{array} { l } x - 3 y \leqslant - 1 \\ x + 2 y \leqslant 9 \\ 3 x + y \geqslant 7 \end{array} \right.$, then the maximum value of $z = 2 x - y$ is \_\_\_\_