$($Ch$\mathrm{.}7\mathrm{.}4$ Prob$)$: A print shop runs a two$-$station binding line, in which the first station

punches holes in the pages and the second station installs the binders. On average, the

punch machine can process $15,000$ pages per hour, while the binder can process

$10,000$ pages per hour. The shop receives work that requires both punching and binding

at a rate of $8,000$ pages per hour. It also receives work requiring only punching at a rate

of $5,000$ pages per hour. Which station is the bottleneck of this line and why? $(20$ pt$,$

Hint: The shop receives work on "punching $+$ binding", also receives work requiring "only

punching".$)$

Compute: $ra(1),ra(2),u(1),u(2)$