Erdős Problem #1129 — Nodes minimizing the Lebesgue constant

For $x_1,\ldots,x_n\in [-1,1]$ let $l_k(x)=\frac{\prod_{i\neq k}(x-x_i)}{\prod_{i\neq k}(x_k-x_i)},$ which are such that $l_k(x_k)=1$ and $l_k(x_i)=0$ for $i\neq k$. Describe which choice of $x_i$ minimise $\Lambda(x_1,\ldots,x_n)=\max_{x\in [-1,1]} \sum_k \lvert l_k(x)\rvert.$