  Let $S=\{n_1,n_2,...,n_t\}$ be a finite set of positive integers with
$\min(S)\geq 3$ and $t\geq 2$. For any positive integers $s_1,s_2,...,s_t$, we
construct a family of 3-uniform bi-hypergraphs ${\cal H}$ with the feasible set
$S$ and $r_{n_i}=s_i, i=1,2,...,t$, where each $r_{n_i}$ is the $n_i$th
component of the chromatic spectrum of ${\cal H}$. As a result, we solve one
open problem for 3-uniform bi-hypergraphs proposed by Bujt\'{a}s and Tuza in
2008. Moreover, we find a family of sub-hypergraphs with the same feasible set
and the same chromatic spectrum as it's own. In particular, we obtain a small
upper bound on the minimum number of vertices in 3-uniform bi-hypergraphs with
any given feasible set.
