1. The problem statement, all variables and given/known data 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 2. Relevant equations I want to find the vector in the set with the maximal length. 3. 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?