Customers arrive according to a Poisson process at a mean rate of $20$ per hour. The service time follows an exponential distribution with a mean rate of $24$ customers per hour. Suppose each server costs $$20$ per hour. The goodwill cost for a customer waiting in line is $$30$ per hour and the goodwill cost for a customer waiting in service is $$10$ per hour. What is the total hourly cost when there are $2$ servers in place? Choose the closest answer.

a$.$

$$54$

b$.$

$$45$

c$.$

$$56$

d$.$

$$47$

e$.$

$$72$