$3$ Combining Tasks

This is going a bit further than we covered in class, but its really interesting $($and hopefully quite

intuitive$).$ Recall the Subway example from the previous section. The metrics are as follows:

An employee has called$-$in sick to work, so the manager now has to combine the toppings and

payment queues. As such, the layout is now a two$-$step process.

Calculate the utilization for the new toppings$/$payment queue. $($Hint: don't over$-$think

this; you can simply add the service times to get the new $($:$E[T_{\text{t}\text{o}\text{p}\text{p}\text{i}\text{n}\text{g}\frac{s}{p}\text{a}\text{y}\text{m}\text{e}\text{n}\text{t}}].$