12. To promote the development of freshwater fish farming in a certain area, the government controls the price within an appropriate range and provides subsidies for freshwater fish farming. Let the market price of freshwater fish be $x$ yuan/kg, and the government subsidy be 1 yuan/kg. According to market research, when $8 \leqslant x \leqslant 14$, the market daily supply $P(\mathrm{~kg})$ and the market daily demand $Q(\mathrm{~kg})$ approximately satisfy the relationship: $P=1000(x+t-8)(x \geqslant 8, t \geqslant 0), Q=500 \sqrt{40-(x-8)^{2}}(8 \leqslant x \leqslant 14)$. The market price when $P=Q$ is called the market equilibrium price.
(1) Express the market equilibrium price as a function of the government subsidy, and find the domain of the function;
(2) To ensure that the market equilibrium price does not exceed 10 yuan/kg, what is the minimum subsidy per kilogram that the government should provide?
12. (1) $1000(x+t-8)=500 \sqrt{40-(x-8)^{2}}$, i.e., $5 x^{2}+(8 t-80) x+\left(4 t^{2}-64 t+\right.$ $280 = 0$. From $\Delta \geqslant 0$ we get $t^{2} \leqslant 50$, at this time $x=8-\frac{4}{5} t \pm \frac{2}{5} \sqrt{50-t^{2}}$. From $\Delta \geqslant 0, t \geqslant 0, 8 \leqslant x \leqslant 14$ we get $\left\{\begin{array}{l}0 \leqslant t \leqslant \sqrt{50} \\ 8 \leqslant 8-\frac{4}{5} t+\frac{2}{5} \sqrt{50-t^{2}} \leqslant 14\end{array}\right.$ or $\left\{\begin{array}{l}0 \leqslant t \leqslant \sqrt{50} \\ 8 \leqslant 8-\frac{4}{5} t-\frac{2}{5} \sqrt{5-t^{2}} \leqslant 14,\end{array}\right.$ we get $0 \leqslant t \leqslant \sqrt{10}$, thus $x=8-\frac{4}{5} t+\frac{2}{5} \sqrt{50-t^{2}}, x \in[0, \sqrt{10}]$;
(2) To make $x \leqslant 10, 8-\frac{4}{5} t+\frac{2}{5} \sqrt{50-t^{2}} \leqslant b$, i.e., $t^{2}+4 t-50 \geqslant 0$, we get $t \geqslant 1$ or $t \leqslant-5$ (discard). Thus $t \geqslant 1$, i.e., the government subsidy is at least 1 yuan per kilogram.