$[10$ pts$]$ A continuous foundation having a width of $1\mathrm{.}5m$ is placed at $1\mathrm{.}0m$ depth within a loose sand deposit where $=17\mathrm{.}0k\frac{N}{m^3}$ and ${}^{\text{'}}=32.$ This sand is underlain by a thick dense sand deposit and ${}^{\text{'}}=40)$ at $2\mathrm{.}5m$ depth below the ground level. Determine the ultimate bearing capacity $(q_u)$ of the foundation.