$*$Please explain all the steps clearly.$*4.$ A small, privately owned Asian company is producing a private$-$label soft drink called Yoggo. A bottling line puts the soft drinks into plastic bottles and then packages the bottles into boxes holding $10$ bottles each. The bottling line is comprised of the following four steps: $(1)$ the bottling machine takes $1$ second to fill a bottle, $(2)$ the lid machine takes $3$ seconds to cover the bottle with a lid, $(3)$ a labeling machine takes $3$ seconds per bottle, and $(4)$ the packaging machine takes $4$ seconds to place a bottle into a box. When a box has Page $64$ been filled with $10$ bottles, a worker tending the packaging machine removes the filled box and replaces it with an empty box. Assume that the time for the worker to remove a filled box and replace it with an empty box is negligible and hence does not affect the capacity of the line. Problem data are summarized in the following table.

a$.$ Draw a process flow diagram of this process. $[\backslash (\backslash$longleftrightarrow $\backslash )$ LO$3-1]$

b$.$ What is the capacity $($bottles$/$hour$)$ at the resource "Apply a lid"? $[$ LO$3-2]$

c$.$ What is the bottleneck in the process? $[\backslash (\backslash$leftrightarrows $\backslash )$ LO$3-4]$

d$.$ Assuming unlimited demand, what would be the flow rate? $[\backslash (\backslash$square $\backslash )$ LO$3-3]$

e$.$ Assuming unlimited demand, what would be the utilization at resource "Apply a lid"? $[$ LO$3-3]$

f$.$ If demand were $12$ bottles per minute, what would be the utilization of bottling? $[$SO$3-3]$

g$.$ If demand were $12$ bottles per minute, what would be the cycle time $($seconds$)$ of the process? $[\backslash (\backslash$square$[\backslash )$ LO$3-3]$

h$.$ Assume the process started empty and that this is a machine$-$paced process. How long would it take to produce $500$ bottles? $[$I LO$3-5]$