Please show all of the math/formulas i.e For capacity show how you got 2,400 etc.

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. 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                     1                             1

Apply a lid                 2                             3

Labeling                    4                             3

Packaging                 3                             4

a. What is the capacity (bottles/hour) at the resource “Apply a lid”?

b. What is the bottleneck in the process?

c. Assuming unlimited demand, what would be the flow rate?

d. Assuming unlimited demand, what would be the utilization at resource “Apply a lid”?

e. Assume the process started empty and that this is a machine-paced process. How long would it take to produce 500 bottles?

f. If each machine is run by one worker, and each worker is paid $10/hour, then what is the cost of direct labor?

g. What is the labor content?

h. Assume that the demand rate is 5000 units/hour, what is the target manpower?