$($Prob$.4)20$ pts$.$

A warehouse takes orders from $8am-4pm.$ The manager wants to analyze the process and

has provided the process flow diagram shown below. 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 the last step is to pack the order for shipping. The store

promises that every order placed today gets shipped next day. So$,$ the picking and packing

operations for all orders should be finished before they go home, which means that the

employees should work overtime if necessary.

$($a$)$ What is the maximum number of orders the store can process without working

overtime?

$($b$)$ How many hours will the picking and packing operations must work if the order taker

works at its maximum capacity? Consider overtime at picking and packing

operations.

$($c$)$ What is the maximum number of orders to be picked?

$($d$)$ If the capacity at order packing operation is doubled, when the order taker works at its

maximum capacity, what are your answers in parts $($a$)$ and $($b$)?$