$1.(15$ points$)$ 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. 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. Problem data are summarized in the following table.

Process Step Number of Machines Seconds per Bottle

Bottling $11$

Apply a lid $13$

Labeling $13$

Packaging $14$

$($a$)$ What is the capacity $($bottles$/$hour$)$ at the resource $$Apply a lid$?(3$ points$)$

$($b$)$ What is the bottleneck in the process? Why? $(3$ points$)$

$($c$)$ Assuming unlimited demand, what would be the flow rate? $(3$ points$)$

$($d$)$ If demand were $12$ bottles per minute, what would be the utilization of bottling? $(3$

points$)$

$($e$)$ If demand were $12$ bottles per minute, what would be the cycle time $($seconds$)$ of the

process? $(3$ points$)$

Make an Excel Table please