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## Homework Statement

Let P be the set of (x,y,z)^t in R^3, which satisfies the following inequalities:

-2x+y+z <=4

x-2y+z<=1

2x+2y-z<=5

x>=1

y>=2

z>=3

## Homework Equations

I want to find the vector in the set with the maximal length.

## The Attempt at a Solution

I have transformed the linear inequalities into matrix form:

(2 -1 -1 -4)

(-1 2 -1 -1)

(-2 -2 1 -5)

I solved it using Gauss elimination and got x = 2, y = 3 and z = 5, which satisfies the linear inequalities.

To find the length of the vector I did : sqr(2^2+3^2+5^2) = sqrt(38), which was my answer.

My instructor says that my solution is not correct. Can anyone help me?