$$(\backslash$mathrm$\{$M$\}/\backslash$mathrm$\{$M$\}/\backslash$mathrm$\{$s$\}/\backslash$mathrm$\{$K$\}$$ Model$).$ Leia is responsible for $13$ data units in the IT offices in a small business called Data Wish. Each data unit runs on an average for $3$ weeks and requires an average of $$1/2$$ or $0\mathrm{.}5$ weeks to get reset by Leia before it can start up again. If we assign the Poisson distribution to the "arrival" of each data unit for service and an exponential distribution to the actual service provided, answer the following questions:

c$.$ If we assign a cost of waiting as $$\backslash$$ $400$$ per week per data unit and $$\backslash$$ $800$$ per week of hiring Leia, what is the Total Time Cost per week cost of servicing the machines? dollars

d$.$ If DataWish decides to hire another individual to help Leia, what would the new total time cost per week be$?$ dollars