An earth embankment is to be constructed with compacted cohesionless soil. The volume of the embankment is $5000 \: m^3$ and the target dry unit weight is $16.2 \: kN/m^3$. Three nearby sites (see figure below) have been identified from where the required soil can be transported to the construction site. The void ratios $(e)$ of different sites are shown in the figure. Assume the specific gravity of soil to be $2.7$ for all three sites. If the cost of transportation per km is twice the cost of excavation per $m^3$ of borrow pits, which site would you choose as the most economic solution (Use unit weight of water $= 10 \: kN/m^3$).
- Site $X$
- Site $Y$
- Site $Z$
- Any of the sites