Consider a serialized process consisting of 4 stages, A, B, C, and D. Currently there is one machine at each stage. Every item must go through all stages.

Stage A is a cleaning process; output rate is 40 units per hour Stage B is a welding process; output rate is 50 units per hour Stage C is a painting station; it takes 2 minutes to finish the job for each unit Stage D is a packing station; each unit takes one minute

Market demand for this product is 41 units per hour (9,840 units per month). The unit profit margin associated with the sales of the product is $7. Also assume the followings:

Additional machines can be acquired and added to any stage. Additional machine is identical to the existing one in the stage. Example: If one machine is added to Stage A (initially 40 units per hour), the output rate of Stage A will increase by 40 units per hour to 40+40=80 units per hour. Cash flows compound monthly to perpetuity, an annual cost of capital of 12% 8 hour daily operation, production is run 30 days per month Answer the following questions:

Part A. Which stage is the bottleneck? What is the current output rate of the process?

Part B. A vendor that services the cleaning machine offers an upgrade to your existing machine at station A. After the upgrade, the machine will simply clean faster. The time spent for each unit will be reduced to 1 minute per unit. If the upgrade cost is a one-time charge of $9,250. Would you consider this upgrade?

Part C. How much are you willing to pay for an additional machine at the bottleneck stage of the current system?

Part D. Suppose the output at stage C is 60/hour. Now, you have an option to rent equipment which will improve the output rate of stage A to 55/hour. The rental cost is $15/hour; would you consider renting this machine for stage A? Why?