Problem $4.(12$ pt in total, $2$pt each$)$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 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.Process Step Number of Machines Seconds per Bottle