# Question: A small privately owned Asian company is producing a private label

A small, privately owned Asian company is producing a private-label soft drink, Yoggo. A machine-paced line puts the soft drinks into plastic bottles and then packages the bottles into boxes holding 10 bottles each. The machine-paced 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 5 seconds to apply a label to a 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. At step 3 there are two labeling machines that each process alternating bottles, that is, the first machine processes bottles 1, 3, 5, . . . and the second machine processes bottles 2, 4, 6, . . .
Problem data are summarized in the table following.
a. What is the process capacity (bottles/hour) for the machine-paced line?
b. What is the bottleneck in the process?
c. If one more identical labeling machine is added to the process, how much is the increase in the process capacity going to be (in terms of bottles/hour)?
d. What is the implied utilization of the packaging machine if the demand rate is 60 boxes/ hour? Recall that a box consists of 10 bottles.

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