Step 1 :The cost of manufacturing $x$ clocks is given by $C(x)=50+27 x-x^{2}$.
Step 2 :The number of clocks that can be produced in $t$ hours is given by $x=2 t$, where $1 \leq t \leq 12$.
Step 3 :We are asked to express $C$ as a function of $t$.
Step 4 :Substitute $x$ with $2t$ in the cost function $C(x)$ to get $C(t)$.
Step 5 :So, $C(t) = 50+27(2t)-(2t)^{2}$.
Step 6 :Simplify to get $C(t)=50+54 t-4 t^{2}$.
Step 7 :The cost function $C(t)$ is given by \(\boxed{C(t)=50+54 t-4 t^{2}}\).