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[VERIFY]

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[PIVOT]

[OUTPUT]

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system
A factory produces components for an instrument, and due to limitations in production capacity and technical levels, some defective products are produced. Experience shows that the number of defective products $P$ (in ten thousand units) is related to the daily production quantity $x$ (in ten thousand units) by the following relation:
$$
P= \left\{
\begin{array}{cl}
\frac {x^{2}}{6}, & \text{for } 1 \leq x < 4, \\
x + \frac {3}{x} - \frac {25}{12}, & \text{for } x \geq 4.
\end{array}
\right.
$$
It is known that every ten thousand units of the qualified components produced can yield a profit of 20,000 yuan, but every ten thousand units of defective products will result in a loss of 10,000 yuan. (Profit = Income - Loss)
(1) Express the factory's daily profit $T$ (in ten thousand yuan) as a function of the daily production quantity $x$ (in ten thousand units);
(2) At what daily production quantity $x$ does the factory maximize its profit, and what is the maximum profit?

Present the answer in LaTex format: \boxed{Your answer}
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