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 $90$ per hour, and packing works at $75$ per hour.

Wally wants to figure out the following.

a$.$ What is the current maximum daily output of the process assuming that no one works overtime? $($i$.$e$.,$ meaning all three operations work a $12-$hour shift$)$

b$.$ How long $($in hours$)$ will the picking and packing operations have to work to finish all the orders that were taken if we have a day where the order taker works at his maximum capacity? $($Round your answers to $1$ decimal place.$)$

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? $($Round your intermediate calculations to $1$ decimal place.$)$

Management is considering doubling the packing capacity $($from $75$ to $150$ orders per hour$).$ Please answer the following based on that change.

e$.$ 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? $($Round your intermediate calculations and final answers to $1$ decimal place.$)$

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

g$.$ Given e$,$ what is the maximum number of orders waiting to be packed?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 $90$ per hour, and

packing works at $75$ per hour.

Wally wants to figure out the following.