For the next $3$ questions, perform a discrete event simulation by hand, like the timeto$-$failure simulation performed in class, or the one from homework $1.$ The system is a single server queue with FIFO service. The state of the system is the number of customers in the queue. Assume the system starts empty and idle, and use interarrival times $($in minutes$)$ from the sequence $(4,2,6,3,1,5,$dots$)$ starting from time $0($i$.$e$.,$ the first arrival is at time $4,$ and the second one is at time $4+2=6).$ All service times are exactly $3\mathrm{.}5$ minutes. Simulate until the table is full. Use as many of the interarrival times as you need.A lathe is used to process an automobile part. The processing time per part is $5$ seconds. After producing $145$ units of the part, the

lathe requires a $48$ second maintenance process. Demand for the part is $10$ units per minute.

What is the maximum inventory of a part $($in units$)?$

Note: Do not round your intermediate calculations. Round your answer to $2$ decimal places.

Maximum inventory $($in units$)$

$\backslash$table$[[$Clock Time,System Status,Next Arrival Time,Next Departure Time$],[0,0,4,$infinity$],[,,$x$.,],[,$y$.,,],[,,,$z$.]]$