A new takeout restaurant in a theme park is in the design process and must decide on how many walk$-$up windows to request in order to minimize the sum of server costs and customer waiting costs. The designer estimates each customer in the system costs $$90$ per hour and a server plus their station costs $$30$ per hour. No more than $6$ walk$-$up windows will fit into the new building.

a$.$ How many walk$-$up windows should be requested if customers arrive at the rate of $64$ per hour and each server at a walk$-$up window can handle $20$ customers per hour? $($Arrival and service rates follow Poisson and exponential distributions respectively$)$

b$.$ A vendor shows the designer new point of sale equipment that would speed up the service rate to $32$ customers per hour but would add a cost of $$20$ per hour to each walk$-$up window $($making the server plus walk$-$up window cost $$50).$ Should the new equipment be implemented and how many walk$-$up windows should be used?