The construction duration for the carpenter to complete the timber structure of the entire house is $16$ weeks $(8$ hours per day$).$ Please perform the following calculations:

a$)$ Calculate the total cost of the timber structure of the house, given the following conditions:

The labor cost for a qualified carpenter is $$120$ per hour $($Monday to Saturday$).$

Saturday's work rate is $1\mathrm{.}5$ times the normal weekday rate.

The floor dimensions of the house are $15,900mm14,500mm.$

The house has four walls, as shown in Figure $1.$

The cost of timber framing materials is $$750$ per $m^2.$