Sum of the perpendicular distances of the vertical feeder lines is .
Graph:
\Graph the function: and label the minimum point.
Observe the graph:
\The sum of perpendicular distances is minimum when .
The equation of the trunk line is .
Substitute .
The equation of the trunk line is .
Find the sum of lengths of the feeder lines when is minimum.
Substitute in
.
Sum of the lengths of the feeder lines is .
The equation of the trunk line is .
Sum of the lengths of the feeder lines is .