Wally$$s Widget Warehouse takes orders from $7$ A$.$M$.$ to $7$ P$.$M$.$ The

manager wants to analyze the process and has provided the following

process flow diagram. There are three steps required to ship a

customer order. The first step is to take the order from a customer. The

second step is to pick the order for the customer, and then they have to

pack the order to ready it for shipping. The order$-$taking step works at

a maximum rate of $100$ customer orders per hour. Order picking works

at a maximum of $80$ per hour, and packing works at $60$ per hour.

Wally wants to figure out the following:

a$.$ What is the current maximum output of the process assuming that no

one works overtime? $($For your answers to these questions, assume

that everyone can start working at $7$ A$.$M$.)$

b$.$ How long will the picking and packing operations have to work if

we have a day where the order taker works at his maximum

capacity all day?

c$.$ Given b$,$ what is the maximum number of orders waiting to be

picked?

d$.$ Given b$,$ what is the maximum number of orders waiting to be

packed?

e$.$ If we double the packing capacity $($from $60$ to $120$ orders per hour$),$

what impact does this have on your answers in parts $($b$),($c$),$ and

$($d$)?$