f[x1_, x2_, x3_] := 1/(Abs[1-x1-x2-x3]^(1-x1-x2-x3) x1^x1 x2^x2 x3^x3)

NMaximize[
    {
    f[x1, x2, x3],
    0<x1<1 && 0<x2<1 && 0<x3<1 && x1 + 2 x2 + 3 x3 < 1
    },
    {x1, x2, x3}
]