Two co$-$working spaces operating in the same busy financial district, WorkHub and OfficeNest, are considering pooling their meeting rooms to accommodate more client bookings and reduce the likelihood of losing clients due to unavailability. WorkHub has $6$ meeting rooms, each used for an average of $2\mathrm{.}5$ hours per booking, while OfficeNest has $4$ meeting rooms with an average booking time of $2$ hours. Both locations are open $10$ hours per day.

WorkHub receives an average of $20$ meeting room booking requests per day, while OfficeNest receives $15$ requests per day. Assume that booking requests arrive following an exponential distribution, where the standard deviation of inter$-$arrival times is equal to the mean.

Due to the presence of other co$-$working spaces in the area, clients are likely to seek meeting rooms elsewhere if none are immediately available. Answer the following questions, showing your calculations and briefly stating any assumptions you make.

A $[25$ pts$].$ Calculate the current probability of losing booking requests and the average utilization of meeting rooms at each co$-$working space individually. If WorkHub and OfficeNest combine their meeting rooms into a shared pool of $10$ rooms, determine how much this pooling would affect booking loss rates and meeting utilization levels.

B $[10$ pts$].$ Briefly discuss the benefits and potential challenges of resource pooling for these co$-$working spaces, with a primary focus on booking efficiency and client satisfaction. You may also consider how your findings and insights from the simulation $$Multiple Server Queues$$ can be applied in this context.