Let x litres ofwater be added to 1125 litres of 45% acid solution.
Then total quantity of mixture = (1125 + x) litres
\(\frac { 45 }{ 100 } \times 1125+0\times \frac { x }{ 100 } >\frac { 25 }{ 100 } \times \left( 1125+x \right) \) and \(\frac { 45 }{ 100 } \times 1125+0\times \frac { x }{ 100 } <\frac { 30 }{ 100 } \times \left( 1125+x \right) \)
Combining the above inequations, we get
\(\frac { 25 }{ 100 } \times 100\le \frac { 2025\times 100 }{ 4(1125+x) } \le \frac { 30 }{ 100 } \times 100\)
\(\Rightarrow\) \(25\le \frac { 50625 }{ 1125+x } \le 30\)
\(\Rightarrow\) \(25\le \frac { 50625 }{ 1125+x } \) and \(\frac { 50625 }{ 1125+x } \le 30\)
\(\Rightarrow\) 28125 + 25x \(\le\) 50625 and 50625 \(\le\)33750 + 30x
\(\Rightarrow\) 25x \(\le\) 22500 and 30x \(\ge\) 1687.5
\(\Rightarrow\) x \(\le\) 900 and x \(\ge\) 562.5
\(\Rightarrow\) 562.5 \(\le\) x \(\le\) 900

The given inequality is x + 2y \(\le\)10.
Draw the graph of the line x + 2y = 10.
Table of values satisfying the equation x+ 2y = 10

x	2	4
y	4	3

Putting (0, 0) in the given inequation, we have 0 + 2 x 0 \(\le\) 10 \(\Rightarrow\) 0 \(\le\) 10, which is true

\(\therefore\) Half plane ofx + 2y \(\le\)10is towards origin.
Also the given inequality is x + y \(\ge\) 1.
Draw the graph of the line x + y = 1.
Table of values satisfying the equation x +y = 1

x	0	1
y	1	0

Putting (0, 0) in the given inequation, we have 0+ 0 \(\ge\) 1\(\Rightarrow\) 0 \(\ge\) 1, which is false.
\(\therefore\) Half plane of x+ y \(\ge\) 1is away from origin.
Also the given inequality is x - y \(\le\) O.
Draw the graph of the line x - y = O.
Table of values satisfying the equation x-y =0

x	1	2
y	1	2

Putting (2, 0) in the given inequation, we have
2 - 0 \(\le\) 0 \(\Rightarrow\) 2 \(\le\) 0 which is false.
\(\therefore\) Half plane ofx - y \(\le\) 0 is away from origin.

The given inequality is 3x + 2y \(\le\)150.
Draw the graph of the line 3x + 2y = 150.
Table of values satisfying the equation 3x + 2y = 150

x	30	40
y	30	15

Putting (0,0) in the given inequation, we have 3 x 0 + 2 x 0 \(\le\)150 \(\Rightarrow\) 0 \(\le\)150, which is true.

\(\therefore\) Half plane of 3x + 2y \(\le\)150 is towards origin.
Also the given inequality is x + 4y \(\le\) 80.
Draw the graph of the line x + 4y = 80.
Table of values satisfying the equation x + 4y = 80

x	0	40
y	20	10

Putting (0, 0) in the given inequation, we have o + 4 x 0 \(\le\) 80 \(\Rightarrow\) 0 \(\le\) 80, which is true.
\(\therefore\) Half plane of x + 4y \(\le\) 80 is towards origin.
The given inequality is x \(\le\)15.
Draw the graph of the line x = 15.
Putting (0, 0) in the given inequation, we have 0 \(\le\)15 which is true
\(\therefore\) Half plane of x \(\le\)15 is towards origin.

The given inequality is x- 2y \(\le\) 3
Draw the graph of the line x -2y = 3

Table of values satisfying the equation x -2y = 3

x	1	5
y	-1	1

Putting (0, 0) in the given inequation, we have o - 2 x 0 \(\le\) 3 \(\Rightarrow\) 0 \(\le\) 3, which is true.
\(\therefore\) Half plane of x - 2y \(\le\)3 is towards origin.
Also the given inequality is 3x + 4y \(\ge\)12.
Draw the graph of the line 3x + 4y = 12.
Table of values satisfying the equation 3x + 4y = 12

x	4	0
y	0	3

Putting (0, 0) in the given inequation, we have 3 x 0 + 4 x 0 \(\ge\) 12 \(\Rightarrow\) 0 \(\ge\) 12, which is false
Half plane of 3x + 4y \(\ge\) 12 is way from origin
The given inequality is y \(\ge\) 1
Draw the graph of the line y = 1
Putting (0, 0) in the given inequation, we have 0 \(\ge\) 1, which is false
half plane is y \(\ge\) 1 is away from origin

The given inequality is 2x +y \(\ge\) 4
Draw the graph of the line 2x + y = 4

Table of values satisfying the equation 2x +y = 4

x	2	1
y	0	2

Putting (0,0) in the given inequation, we have 2 x 0 + 0 \(\ge\) 0 \(\Rightarrow\) 0 \(\ge\)4, which is false
\(\therefore\) Half plane of 2x +y \(\ge\)4 is awy from origin
Also the given inequality is x + Y \(\le\)3.
Draw the graph of the line x + y = 3.
Table of values satisfying the equation x +y = 3

x	2	1
y	1	2

The putting (0,0) in the given inequation, we have 0 + 0 \(\le\) 3 \(\Rightarrow\) 0 \(\le\) 3, Which is true

\(\therefore\) Half plane inequality is 2x - 3y \(\le\)6
Table of values satisfyinh the equation 2x -3y = 6

x	0	3
y	-2	0

Putting (0, 0) in the given inequation, we have 2 x 0 -3 x 0 \(\le\) 6 \(\Rightarrow\) 0 \(\le\) 6, which is true
\(\therefore\) Half plane of 2x -3y \(\le\)6 is towards origin

The given inequality 5x +4y \(\le\) 20
draw the graph of the line 5x + 4y = 20

table of values satisfying the equation 5x +4y = 20

x	4	0
y	0	5

Putting (0,0) in the given inequation, we have 5 x 0 +4 x 0 \(\le\) 20 \(\Rightarrow\) 0 \(\le\) 20, which is true
\(\therefore\) Half plane of 5x +4y \(\le\) 20 is towards origin
Also the given inequality ix x \(\ge\) 1
Draw the graph of the line x = 1
Putting (0,0) in the given inequation, we have 0 \(\ge\) 1 which is false
\(\therefore\) Half plane of x \(\ge\) 1 is away from origin
the given inequality is y \(\ge\) 2
Draw the graph of the line y = 2
Putting (0,0) in the given inequation, we have 0 \(\ge\)2, which is false
\(\therefore\) half plane y \(\ge\) 2 is away from origin

The given inequality is 2x + y \(\ge\) 8
Draw the graph of the line 2x +y = 8

Table of values satisfying the eqaution we have
2x +y = 8

x	3	4
y	2	0

Putting (0,0) in the given inequation, we have
2 x 0 + 0 \(\ge\) 8 \(\Rightarrow\) 0 \(\ge\)8, which is false
\(\therefore\) Half plane of 2x +y  \(\ge\) 8 is away from origin
Also the given inequality is x + 2y 
Draw the graph of the line x +2y = 10
Table of the values satisfying the equation x + 2y = 10

x	2	4
y	4	3

Putting (0,0) in the given inequation , we have 0 + 2 x 0 \(\ge\) 10 \(\Rightarrow\) 0 \(\le\) 10, Which is false
\(\therefore\) half plane of x +2y \(\ge\) 10 is away from origin 

The given inequality is x + y \(\le\) 6
Draw the graph of the line x + y = 6.

Table of value satisfying the equation x + y = 6

x	3	4
y	3	2

Putting (0, 0) in the given inequation, we have
0 + 0 \(\le\) 6 \(\Rightarrow\) 0 \(\le\) 6, which is true
Half plane of x +y \(\le\) 6 is towards origin
Also the given unequality is x +y \(\ge\)4
Draw the graph of the line x + y = 4
Table of values satisfying the equation x + y = 4

x	2	1
y	2	3

Putting (0, 0) in the given inequation, we have 0 + 0 \(\ge\) 4 \(\Rightarrow\) 0 \(\ge\) 4, which is false
Hald plane of x +y \(\ge\) 4 is awy from origin

The given inequality ix x + y \(\ge\) 4
Draw the gtaph of the line x + y = 4

Total of value satisfying the equation x +y = 4

x	3	2
y	1	2

Putting (0, 0) in the given inequation, we have 0 + 0 \(\ge\) 4 \(\Rightarrow\) 0 \(\ge\) 4 which is false
\(\therefore\) Half plane of x + y \(\ge\) 4 is away from origin
Also the given inequality is 2x - y > o.
Draw the graph of the line 2x - y = o.
Table of values satisfying the equation
2x -y =0

x	1	2
y	2	4

Putting (3, 0) in the given inequation, we have
2 x 3 - 0 > 0 => 6 > 0, which is true.
\(\therefore\) Half plane of 2x - y > 0 containing (3,0)

2x + y≥ 6 … (1)
3x + 4y ≤ 12 … (2)
The graph of the lines, 2x + y= 6 and 3x + 4y = 12, are drawn in the figure below.
Inequality (1) represents the region above the line, 2x + y= 6 (including the line 2x + y= 6), and inequality (2) represents the region below the line, 3x + 4y =12 (including the line 3x + 4y =12).
Hence, the solution of the given system of linear inequalities is represented by the common shaded region including the points on the respective lines as follows.