Unbounded solution
In maximization problem, if shaded area is open-ended. This means that the maximization is not possible and the LPP has no finite solution. Hence the solution of the given problem is unbounded.

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Example
Find solution using graphical method
MAX Z = 5X1 + 4X2
subject to
X1 - 2X2 <= 1
X1 + 2X2 >= 3
and X1,X2 >= 0

Solution:
Problem is

MAX `Z` `=` `` `5` `X_1` ` + ` `4` `X_2`

subject to

`` `` `X_1` ` - ` `2` `X_2` ≤ `1` `` `` `X_1` ` + ` `2` `X_2` ≥ `3`

and `X_1,X_2 >= 0; `

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Hint to draw constraints

1. To draw constraint `color{red}{X_1-2X_2<=1} ->(1)`

Treat it as `color{red}{X_1-2X_2=1}`

When `X_1=0` then `X_2=?`

`=>(0)-2X_2=1`

`=>-2X_2=1`

`=>X_2=(1)/(-2)=-0.5`

When `X_2=0` then `X_1=?`

`=>X_1-2(0)=1`

`=>X_1=1`

`X_1`	0	1
`X_2`	-0.5	0

Put `X_1=0,X_2=0` (origin) in `color{red}{X_1-2X_2<=1}`, then `0+0<=1`, which is true,

The half plane containing the origin is the region of the solution set of the inequation `color{red}{X_1-2X_2<=1}`

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2. To draw constraint `color{green}{X_1+2X_2>=3} ->(2)`

Treat it as `color{green}{X_1+2X_2=3}`

When `X_1=0` then `X_2=?`

`=>(0)+2X_2=3`

`=>2X_2=3`

`=>X_2=(3)/(2)=1.5`

When `X_2=0` then `X_1=?`

`=>X_1+2(0)=3`

`=>X_1=3`

`X_1`	0	3
`X_2`	1.5	0

Put `X_1=0,X_2=0` (origin) in `color{green}{X_1+2X_2>=3}`, then `0+0>=3`, which is false,

The half plane not containing the origin is the region of the solution set of the inequation `color{green}{X_1+2X_2>=3}`

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The value of the objective function at each of these extreme points is as follows:

Extreme Point Coordinates (`X_1`,`X_2`)	Lines through Extreme Point	Objective function value `Z=5X_1 + 4X_2`
`color{red}{A(0,1.5)}`	`color{green}{2->X_1+2X_2>=3}` `color{black}{3->X_1>=0}`	`5(0)+4(1.5)=6`
`color{green}{B(2,0.5)}`	`color{red}{1->X_1-2X_2<=1}` `color{green}{2->X_1+2X_2>=3}`	`5(2)+4(0.5)=12`

Problem has an unbounded solution.

Note: In maximization problem, if shaded area is open-ended. This means that the maximization is not possible and the LPP has no finite solution. Hence the solution of the given problem is unbounded.

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