The cost of waiting in Problem $1$ is $$5\mathrm{.}00$ per unit per period, and the service facility costs $$2\mathrm{.}50$ per unit served.

a$)$ What is the total system cost $($TC$)?$

b$)$ If the service rate is doubled at a cost of $$3\mathrm{.}50$ per unit served, what is the total system cost $($TC$)?$