# Linear Optimization Problem

#### goosey00

##### Member

Maximize: z=2x2+5x2+x3
x1+x2+x3 less then or equal to 12
x1-x2 less then or equal to 15
x2+2x3 less then or equal to 10
x1, x2 and x3 is greater then or equal to 0
x1= x2= x3= s1= s2= s3= z=
I get x1=2, x2=10 x3=0 s1=0 s2=0 s3=0 z=0
Is this wrong??

Last edited:

#### Opalg

##### MHB Oldtimer
Staff member
Re: Linear Optimization Problem follow up

Maximize: z=2x2+5x2+x3 I assume that the first x2 should be x1.
x1+x2+x3 less then or equal to 12
x1-x2 less then or equal to 15
x2+2x3 less then or equal to 10
x1, x2 and x3 is greater then or equal to 0
x1= x2= x3= s1= s2= s3= z=
I get x1=2, x2=10 x3=0 s1=0 s2=0 s3=0 z=0
Is this wrong??
It looks as though $x_1=2,\ x_2=10,\ x_3=0$ is correct, but why do you get $z=0$? The condition $z=2x_1+5x_2+x_3$ says that $z$ should be 54 for those values of the $x$'s.

#### goosey00

##### Member
Re: Linear Optimization Problem follow up

It looks as though $x_1=2,\ x_2=10,\ x_3=0$ is correct, but why do you get $z=0$? The condition $z=2x_1+5x_2+x_3$ says that $z$ should be 54 for those values of the $x$'s.
So where do you get 54?
BTW-you are right, it was suppose to be 1.

#### Jameson

Staff member
Re: Linear Optimization Problem follow up

So where do you get 54?
BTW-you are right, it was suppose to be 1.
If you plug in $x_1=2$, $x_2=10$ and $x_3=0$ into $z=2x_1+5x_2+x_3$ you get $z=(2 \times 2) + (5 \times 10) + 0=54$.

#### Sudharaka

##### Well-known member
MHB Math Helper
Re: Linear Optimization Problem follow up

Maximize: z=2x2+5x2+x3
x1+x2+x3 less then or equal to 12
x1-x2 less then or equal to 15
x2+2x3 less then or equal to 10
x1, x2 and x3 is greater then or equal to 0
x1= x2= x3= s1= s2= s3= z=
I get x1=2, x2=10 x3=0 s1=0 s2=0 s3=0 z=0
Is this wrong??
Hi goosey00,

You can check the optimal solutions of linear programming problems >>here<<.

Kind Regards,
Sudharaka.