Maximization in 2018 Variables

Notice that since $f$ is a linear function in every one of it's variables, its maximum value is achieved when every $x_k$ is either $1$ or $0$ . If we have $k$ zeroes and $2018-k$ ones, then $f(x_1, ..., x_k) = 2018 - k$ if $k > 0$ and $f(x_1, ..., x_k) = 2017$ if $k = 0$ . Either way, the maximum value of $f$ is $\boxed{2017}$ .