The parts department of a large automobile dealership has a counter used exclusively for mechanics' requests for parts. The time between requests can be modeled by a negative exponential distribution. Customers arrive at a rate of $8$ per hour. A clerk can handle requests at a rate of $5$ per hour, and this can be modeled by a Poisson distribution. Clerks cost $$10$ per hour and mechanics cost $$40$ per hour. Use Table $18-4.$

a$.$ Determine the cost of capacity and waiting if the parts department hires $2,3$ or $4$ clerks. $($Round Ls to $3$ decimals. Round costs to $2$ decimals.$)$

b$.$ Based on your response in part a$,$ how many clerks should be hired?