5. {3 pts) An operator finishes a batch of assembled parts working at a rate of 60 parts per hour. This same operator nishes a second batch of parts at a rate of 90 parts per hour. Assmning both batches were of the same size, what is the operator's average assembly rate? 6. (24 pts) Suppose the processing times for an automated (once the machine is running it doesn't require operator involvement) machining operation have the following discrete distribution: _--n a. (6 pts) What is the average time for the machine to process a part? b. (6 pts) What is the standard deviation of the processing time? c. Suppose four parts are produced using this machining operation. c.i. (6 pts) What is the probability that each of the four parts is made in 4.5 minutes or less? Have you made any assumptions? Explain. c.ii. {6 pts) What is the probability that three or more of the parts are each made in 4.5 minutes or less? Have you made any assumptions? Explain. 7. {20 pts) ln Cell 8 at Respiratory Therapeutics they produce Subassembly 417 that is used in one of their breathing assist products. Cell 8 contains 1) an injection molding machine, 2] assembly benches for completing assembly operations that use the plastics parts from the injection molding machines plus additional components purchased from outside vendors, and 3] a testing station that tests completed Subassembly 4173 to insure they are ready to go into the breathing assist products. Currently there is one injection molding machine that has a mold with six cavities (which means it makes six parts every machine cycle) and its machine cycle time is 45 seconds. The injection molding process is fully automated and requires no operator intervention. The assembly process for Subassemhly 417 requires 21 seconds and is a manual process with one operator per assembly station- The testing process requires an operator to properly position a Subassemhly 417 in the testing station, which takes 10' seconds, then the test time is 84 seconds which requires no operator intervention, and then it takes an operator 5 seconds to unload the subassembly. The testing station can hold 15 Subassembly 417s and is designed such that different subassemblies can start testing at different times (they do not have to be started at the same time.) Currently, Respiratory Therapeutics has chosen to have each assembly operator perform the necessary testing station activities for the subassemblies that hefshe built. Answer the following questions, consider parts a to c separately. a. If there are 3 assembly operators what is the output of Subassembly 4175 from Cell 8? b. It is relatively inexpensive to add additional assembly stations- If the only thing you can change is the number of assembly stations and assembly operators in Cell 8, how many of each are needed to maximize the output of Cell 8? c. Due to increased demand for their breathing assist products, Respiratory Therapeutics wants to increase the output of Cell 8. Due to space limitations there