A trapezoidal channel is designed as the main hydraulic structure to carry $Q=8\mathrm{.}0\frac{m^3}{s}$ at $S_0=0\mathrm{.}0012,n=0\mathrm{.}017,$ and $m=1\mathrm{.}0.$ The unit cost of the base lining material and side$-$lining material are respectively $$40$ per $m^2,$ and $$45$ per $m^2.$ The combined cost of the corner materials is $$8\mathrm{.}0$ per meter. $[25$ Marks$]$

$2\mathrm{.}1$ Proportion the canal section using the minimum lining cost approach, $($Note: No need to check for flow velocity and Froud Number$).[15$ Marks$]$

$2\mathrm{.}2$ Determine the total cost of the concrete lining if Freeboard is $F_b=0\mathrm{.}75m.[10$ Marks$]$