  We consider a problem where agents have private positions on a line, and
public approval preferences over two facilities, and their cost is the maximum
distance from their approved facilities. The goal is to decide the facility
locations to minimize the total and the max cost, while incentivizing the
agents to be truthful. We design a strategyproof mechanism that is
simultaneously $11$- and $5$-approximate for these two objective functions,
thus improving the previously best-known bounds of $2n+1$ and $9$.
