$3$ 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:

$\backslash$table$[[,$Bread queue,Toppings queue,Payment queue$],[$Queue structure,one $\frac{M}{M}\frac{?}{1}$ queue,one $\frac{M}{M}\frac{?}{1}$ queue,one $\frac{M}{M}\frac{?}{1}$ queue$],[$Arrival rate,$$ per minute,$$ per minute,$$ per minute$],[$Service time,$E[T]=2$ minutes,$E[T]=1\mathrm{.}5$ minutes,$E[T]=0\mathrm{.}5$ minutes$]]$

What is the average number of customers in the two$-$step process $($bread queue and toppings$/$payment queue$),E[L_{\text{b}\text{r}\text{e}\text{a}\text{d}}+L_{\text{t}\text{o}\text{p}\text{p}\text{i}\text{n}\text{g}\frac{s}{p}\text{a}\text{y}\text{m}\text{e}\text{n}\text{t}}]?$ Comparing your answer to question $14,$ what do you notice?