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Operating labor requirements $L$ in the chemical process industry is described in terms of the plant capacity $C ( \text{kg day}^{-1})$ over a wide range $(10^3-10^6)$ by a power law relationship $$L=\alpha C^{\beta}$$ where $\alpha$ and $\beta$ are constants. It is known that

- $L$ is $60$ when $C$ is $2 \times 10^4$
- $L$ is $70$ when $C$ is $6 \times 10^4$

The value of $L$ when $C$ is $10^5 \text{ kg day}^{-1}$ is _______(round off to nearest integer).