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 $120$ customer orders per hour. Order picking works at a maximum of $100$ per hour, and packing works at $80$ per hour.

A flow chart. Step $1.$ Customers. Step $2.$ Take orders, $120$ customers per hour. Step $3.$ Customer orders. Step $4.$ Pick orders, $100$ customers per hour. Step $5.$ Picked orders. Step $6.$ Pack orders, $80$ customers per hour. Step $7.$ Wait for the shipper.

Wally wants to figure out the following.

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$.)$

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?

Note: Round your answers to $1$ decimal place.

Given b$,$ what is the maximum number of orders waiting to be picked?

Given b$,$ what is the maximum number of orders waiting to be packed?

Note: Round your intermediate calculations to $1$ decimal place.

Management is considering doubling the packing capacity $($from $80$ to $160$ orders per hour$).$ Please answer the following based on that change.

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?

Note: Round your intermediate calculations and final answers to $1$ decimal place.

Given e$,$ what is the maximum number of orders waiting to be picked?

Given e$,$ what is the maximum number of orders waiting to be packed?