PLEASE DO THE CALCULATIONS FOR ME STEP BY STEP. I NEED CALCULATIONS, NOT EXPLANATIONS. Thanks

The director of a large engineering department is considering the rental of several

computer terminals to provide the staff with access to a shared database. Based on an

intradepartmental survey, the director has gathered the following information:

$$ The department generates approximately $8$ database requests per hour.

$$ Each database search takes an average of $15$ minutes $(0\mathrm{.}25$ hours$)$ to complete.

$$ The cost of renting a computer terminal is $$10$ per hour.

$$ The cost of keeping an engineer idle $($while they wait for an available terminal$)$ is

$$30$ per hour.

The director assumes that:

$$ The arrival of database requests follows a Poisson distribution.

$$ The time it takes to process a request $($service time$)$ follows an exponential

distribution.

a$)$ Based on the information provided, determine how many computer terminals the

director should rent in order to minimize the total costs for the department. $[30$ marks$]$

b$)$ Draw a flowchart showing your proposed queuing system $[5$ marks$]$

c$)$ Under the system you proposed in part $($a$),$ calculate the expected waiting time for

an engineer before they can access a terminal to begin their database search. $[5$ marks$]$