1. The problem statement, all variables and given/known data Using Lagrange multipliers, find the max and the min values of f: f(x,y,z) = x^2 +2y^2+3x^2 Constraints: x + y + z =1 x - y + 2z = 2 2. Relevant equations ∇f(x) = λ∇g(x) + μ∇h(x) 3. The attempt at a solution Using Lagrange multipliers, I obtained the equations: 2x = λ + μ 4y = λ - μ 6z = λ + 2μ With the constraints, I tried to find values for the unknowns, but I can't solve the system of equations. I don't know where to go from here. Can anyone help put? Any input is appreciated!