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[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

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A company in our city's university student entrepreneurship incubation base produces a kind of tourism commodity with the characteristic of "Confucianism Zoucheng". The company's annual fixed cost is 100,000 yuan, and an additional investment of 27,000 yuan is required for every thousand pieces produced. Suppose the company produces and sells $x$ thousand pieces of this tourism commodity within a year, and the sales revenue per thousand pieces is $R(x)$ in ten thousand yuan, satisfying the function relationship:
$$
R(x)=\begin{cases}
10.8- \frac{{x}^{2}}{30}, & 0 < x\leqslant 10 \\
\frac{108}{x}- \frac{1000}{3{x}^{2}}, & x > 10
\end{cases}
$$

$(1)$ Write the analytical expression of the annual profit $W$ (in ten thousand yuan) as a function of $x$ (in thousand pieces) for this tourism commodity;  
$(2)$ At what production volume (in thousand pieces) does the company achieve the maximum annual profit from the production of this tourism commodity?

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