Problem $6(20$ points$)$

A water quality depth of $2cm$ from a $1-$hectare catchment in a municipality is to be treated by an

exfiltration trench. The land allocated for the trench is $100$ meters long and sits between the road and a

popular walking path. The surrounding soil has a hydraulic conductivity of $1\frac{m}{d}$ and a porosity of $0\mathrm{.}35.$

The trench cannot exceed a depth of $1$ meter in order to avoid affecting other subsurface infrastructure.

Find three alternatives for trench dimensions $(LxWxH,$ one that minimizes width, one that minimizes

length, and one the minimizes depth. All alternatives must drain completely within $38$ hours.