Four walkers and one lantern on a narrow bridge

Four people must cross a bridge at night. At most two can be on it at once, they share a single lantern that must accompany every crossing, and a pair moves at the slower person's speed. Individually they need $1$, $2$, $5$ and $10$ minutes. What is the shortest total time to get everyone across?

$17$ minutes. Send $1$ and $2$ over ($2$), bring $1$ back ($1$), send $5$ and $10$ together ($10$), bring $2$ back ($2$), and send $1$ and $2$ again ($2$). Pairing the two slowest saves more than having the fastest escort everyone ($19$).