Warehouse takes orders from $8$:$00$ A$.$M$.$ to $8$:$00$ P$.$M$.$ The manager wants to analyze the process and has provided the following process flow diagram. Three steps are 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 to make it ready to ship to the customer. CentralMart promises that every order placed today gets shipped tomorrow. That means the picking and packing operations must finish all orders before they go home, i$.$e$.,$ picking and packing may operate $24$ hours per day.

Capacities

Take Orders $100$ customer orders per hour

Pick Orders $80$ customer orders per hour

Pack Orders $60$ customer orders per hour

a$.$ What is the current maximum output of the process?

b$.$ How long will picking and packing operations have to work if we have a day where the order taker works at maximum capacity.

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

d$.$ Given b above, 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 to $($b$),($c$)$ and $($d$)?$