12. (12 points) A bank in an island country operates from $9:00 \sim 17:00$ every day. Under normal circumstances, it prepares 500,000 yuan in cash at $9:00$ every day. Assuming the withdrawal amount per hour is the same, and the deposit amount per hour is also the same, by $17:00$ when it closes, there is 600,000 yuan in cash. If the withdrawal amount per hour is four times the normal amount, the bank will run out of cash by $14:00$. If the withdrawal amount per hour is ten times the normal amount, and the deposit amount is reduced to half of the normal amount, to ensure that there is still 500,000 yuan in cash at $17:00$ when it closes, how much cash (in ten thousand yuan) should be prepared at $9:00$ when it opens?
【Solution】From 9:00 to 17:00 is 8 hours, from 9:00 to 14:00 is 5 hours, $(60 - 50) \div 8=1.25$ (ten thousand yuan/hour),
$$
50 \div 5=10 \text { (ten thousand yuan/hour), }
$$

The withdrawal speed is:
$$
\begin{aligned}
& (10+1.25) \div(4-1), \\
= & 11.25 \div 3, \\
= & 3.75 \text { (ten thousand yuan/hour), }
\end{aligned}
$$

The deposit speed is:
$$
\begin{array}{l}
3.75+1.25=5 \text { (ten thousand yuan/hour), } \\
(3.75 \times 10-5 \div 2) \times 8+50, \\
=(37.5-2.5) \times 8+50, \\
=35 \times 8+50, \\
=280+50, \\
=330 \text { (ten thousand yuan) }.
\end{array}
$$

Answer: 330 ten thousand yuan in cash needs to be prepared.