$\"\"$

Sum of the squares of the lengths of the vertical feeder lines is $\"\"$ .

From the graph, equation of the trunk line is $\"\"$ .

Consider $\"\"$ .

Apply derivative on each side with respect to $\"\"$ .

$\"\"$

To minimizing sum function equate $\"\"$ to zero.

$\"\"$

Equation of the trunk line is $\"\"$ .

$\"\"$

Sum of the lengths of the feeder lines is $\"\"$ .

Substitute $\"\"$ in above expression.

$\"\"$

Equation of the trunk line is $\"\"$ .

Sum of the lengths of the feeder lines is $\"\"$ .