Question 59
Let $ABC$ be a triangle with $AB=13$, $BC=14$, $CA=15$. Company XYZ wants to locate their base at the point $P$ in the plane minimizing the total distance to their workers, who are located at vertices $A$, $B$, and $C$. There are $1$, $5$, and $4$ workers at $A$, $B$, and $C$, respectively. Find the minimum possible total distance Company XYZ's workers have to travel to get to $P$.
