A tech support company based in Switzerland has established a global service center with technicians based in China with a strong technical talent pool and competitive wages. These technicians remotely troubleshoot customer issues. On average, resolving a customer issue takes $20$ minutes. The company maintains a team of $4$ technicians available at any given time. Customer support tickets arrive every $5$ minutes on average, with some variation $($standard deviation of $5$ minutes$).$ When a technician becomes available, they are assigned the next ticket. The company charges the customer CHF $50$ for the support session and pays the technician CHF $25$ for resolving the issue, resulting in a CHF $25$ profit. However, if all technicians are occupied, the company has to redirect the issue to a local technician within the company. While the customer receives the needed support, the company incurs the full cost of CHF $50$ for the local technician's time and makes no profit on that interaction.

Question $1$:$$

What is the probability of a customer$$s issue being addressed by a technician in China? $($Round to four decimal places$)$

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Question $2$:$$

What would be the additional revenue per hour obtained if the company managed to have $10$ technicians in China on duty at any given time? $($Round to the nearest integer$)$

Answer in CHF$/$hour

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Question $3$:

What would be the additional profit per hour if the company managed to have $10$ technicians in China on duty at any given time? $($Round to the nearest integer$)$

Answer in CHF$/$hour